Jump to navigation Jump to search

General

Display information for equation id:math.242901.10 on revision:242901

* Page found: Flow (mathematics) (eq math.242901.10)

(force rerendering)

Occurrences on the following pages:

Hash: 9223f42735c0121dad5890b6462adcba

TeX (original user input):

 \dot{\boldsymbol{y}}(s) = \boldsymbol{G}(\boldsymbol{y}(s)), \qquad \boldsymbol{y}(0)=(\boldsymbol{x}_0,t_0)

TeX (checked):

{\dot {\boldsymbol {y}}}(s)={\boldsymbol {G}}({\boldsymbol {y}}(s)),\qquad {\boldsymbol {y}}(0)=({\boldsymbol {x}}_{0},t_{0})

LaTeXML (experimental; uses MathML) rendering

MathML (6.66 KB / 1.131 KB) :

𝒚 ˙ ( s ) = 𝑮 ( 𝒚 ( s ) ) , 𝒚 ( 0 ) = ( 𝒙 0 , t 0 ) formulae-sequence ˙ 𝒚 𝑠 𝑮 𝒚 𝑠 𝒚 0 subscript 𝒙 0 subscript 𝑡 0 {\displaystyle{\dot{{\boldsymbol{y}}}}(s)={\boldsymbol{G}}({\boldsymbol{y}}(s)% ),\qquad{\boldsymbol{y}}(0)=({\boldsymbol{x}}_{0},t_{0})}
<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\dot{{\boldsymbol{y}}}}(s)={\boldsymbol{G}}({\boldsymbol{y}}(s)%&#10;),\qquad{\boldsymbol{y}}(0)=({\boldsymbol{x}}_{0},t_{0})}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.27" xref="p1.1.m1.1.27.1.cmml">
      <mrow id="p1.1.m1.1.27.2" xref="p1.1.m1.1.27.2.cmml">
        <mrow id="p1.1.m1.1.27.2.1" xref="p1.1.m1.1.27.2.1.cmml">
          <mover accent="true" id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
            <mi id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">𝒚</mi>
            <mo id="p1.1.m1.1.1.1" xref="p1.1.m1.1.1.1.cmml">˙</mo>
          </mover>
          <mo id="p1.1.m1.1.27.2.1.1" xref="p1.1.m1.1.27.2.1.1.cmml"></mo>
          <mrow id="p1.1.m1.1.27.2.1.2" xref="p1.1.m1.1.27.2.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.2" xref="p1.1.m1.1.27.2.1.cmml">(</mo>
            <mi id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">s</mi>
            <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.27.2.1.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">=</mo>
        <mrow id="p1.1.m1.1.27.2.2" xref="p1.1.m1.1.27.2.2.cmml">
          <mi id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">𝑮</mi>
          <mo id="p1.1.m1.1.27.2.2.1" xref="p1.1.m1.1.27.2.2.1.cmml"></mo>
          <mrow id="p1.1.m1.1.27.2.2.2" xref="p1.1.m1.1.27.2.2.2.2.cmml">
            <mo stretchy="false" id="p1.1.m1.1.7" xref="p1.1.m1.1.27.2.2.2.2.cmml">(</mo>
            <mrow id="p1.1.m1.1.27.2.2.2.2" xref="p1.1.m1.1.27.2.2.2.2.cmml">
              <mi id="p1.1.m1.1.8" xref="p1.1.m1.1.8.cmml">𝒚</mi>
              <mo id="p1.1.m1.1.27.2.2.2.2.1" xref="p1.1.m1.1.27.2.2.2.2.1.cmml"></mo>
              <mrow id="p1.1.m1.1.27.2.2.2.2.2" xref="p1.1.m1.1.27.2.2.2.2.cmml">
                <mo stretchy="false" id="p1.1.m1.1.9" xref="p1.1.m1.1.27.2.2.2.2.cmml">(</mo>
                <mi id="p1.1.m1.1.10" xref="p1.1.m1.1.10.cmml">s</mi>
                <mo stretchy="false" id="p1.1.m1.1.11" xref="p1.1.m1.1.27.2.2.2.2.cmml">)</mo>
              </mrow>
            </mrow>
            <mo stretchy="false" id="p1.1.m1.1.12" xref="p1.1.m1.1.27.2.2.2.2.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo rspace="22.5pt" id="p1.1.m1.1.13" xref="p1.1.m1.1.27.1a.cmml">,</mo>
      <mrow id="p1.1.m1.1.27.3" xref="p1.1.m1.1.27.3.cmml">
        <mrow id="p1.1.m1.1.27.3.1" xref="p1.1.m1.1.27.3.1.cmml">
          <mi id="p1.1.m1.1.15" xref="p1.1.m1.1.15.cmml">𝒚</mi>
          <mo id="p1.1.m1.1.27.3.1.1" xref="p1.1.m1.1.27.3.1.1.cmml"></mo>
          <mrow id="p1.1.m1.1.27.3.1.2" xref="p1.1.m1.1.27.3.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.16" xref="p1.1.m1.1.27.3.1.cmml">(</mo>
            <mn id="p1.1.m1.1.17" xref="p1.1.m1.1.17.cmml">0</mn>
            <mo stretchy="false" id="p1.1.m1.1.18" xref="p1.1.m1.1.27.3.1.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">=</mo>
        <mrow id="p1.1.m1.1.27.3.2" xref="p1.1.m1.1.27.3.2.1.cmml">
          <mo stretchy="false" id="p1.1.m1.1.20" xref="p1.1.m1.1.27.3.2.1.cmml">(</mo>
          <msub id="p1.1.m1.1.27.3.2.2" xref="p1.1.m1.1.27.3.2.2.cmml">
            <mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">𝒙</mi>
            <mn id="p1.1.m1.1.22.1" xref="p1.1.m1.1.22.1.cmml">0</mn>
          </msub>
          <mo id="p1.1.m1.1.23" xref="p1.1.m1.1.27.3.2.1.cmml">,</mo>
          <msub id="p1.1.m1.1.27.3.2.3" xref="p1.1.m1.1.27.3.2.3.cmml">
            <mi id="p1.1.m1.1.24" xref="p1.1.m1.1.24.cmml">t</mi>
            <mn id="p1.1.m1.1.25.1" xref="p1.1.m1.1.25.1.cmml">0</mn>
          </msub>
          <mo stretchy="false" id="p1.1.m1.1.26" xref="p1.1.m1.1.27.3.2.1.cmml">)</mo>
        </mrow>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.27.1.cmml" xref="p1.1.m1.1.27">
        <csymbol cd="ambiguous" id="p1.1.m1.1.27.1a.cmml" xref="p1.1.m1.1.13">formulae-sequence</csymbol>
        <apply id="p1.1.m1.1.27.2.cmml" xref="p1.1.m1.1.27.2">
          <eq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/>
          <apply id="p1.1.m1.1.27.2.1.cmml" xref="p1.1.m1.1.27.2.1">
            <times id="p1.1.m1.1.27.2.1.1.cmml" xref="p1.1.m1.1.27.2.1.1"/>
            <apply id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
              <ci id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.1">˙</ci>
              <ci id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">𝒚</ci>
            </apply>
            <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝑠</ci>
          </apply>
          <apply id="p1.1.m1.1.27.2.2.cmml" xref="p1.1.m1.1.27.2.2">
            <times id="p1.1.m1.1.27.2.2.1.cmml" xref="p1.1.m1.1.27.2.2.1"/>
            <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝑮</ci>
            <apply id="p1.1.m1.1.27.2.2.2.2.cmml" xref="p1.1.m1.1.27.2.2.2">
              <times id="p1.1.m1.1.27.2.2.2.2.1.cmml" xref="p1.1.m1.1.27.2.2.2.2.1"/>
              <ci id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">𝒚</ci>
              <ci id="p1.1.m1.1.10.cmml" xref="p1.1.m1.1.10">𝑠</ci>
            </apply>
          </apply>
        </apply>
        <apply id="p1.1.m1.1.27.3.cmml" xref="p1.1.m1.1.27.3">
          <eq id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19"/>
          <apply id="p1.1.m1.1.27.3.1.cmml" xref="p1.1.m1.1.27.3.1">
            <times id="p1.1.m1.1.27.3.1.1.cmml" xref="p1.1.m1.1.27.3.1.1"/>
            <ci id="p1.1.m1.1.15.cmml" xref="p1.1.m1.1.15">𝒚</ci>
            <cn type="integer" id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17">0</cn>
          </apply>
          <interval closure="open" id="p1.1.m1.1.27.3.2.1.cmml" xref="p1.1.m1.1.27.3.2">
            <apply id="p1.1.m1.1.27.3.2.2.cmml" xref="p1.1.m1.1.27.3.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.27.3.2.2.1.cmml" xref="p1.1.m1.1.27.3.2.2">subscript</csymbol>
              <ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">𝒙</ci>
              <cn type="integer" id="p1.1.m1.1.22.1.cmml" xref="p1.1.m1.1.22.1">0</cn>
            </apply>
            <apply id="p1.1.m1.1.27.3.2.3.cmml" xref="p1.1.m1.1.27.3.2.3">
              <csymbol cd="ambiguous" id="p1.1.m1.1.27.3.2.3.1.cmml" xref="p1.1.m1.1.27.3.2.3">subscript</csymbol>
              <ci id="p1.1.m1.1.24.cmml" xref="p1.1.m1.1.24">𝑡</ci>
              <cn type="integer" id="p1.1.m1.1.25.1.cmml" xref="p1.1.m1.1.25.1">0</cn>
            </apply>
          </interval>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle{\dot{{\boldsymbol{y}}}}(s)={\boldsymbol{G}}({\boldsymbol{y}}(s)%
),\qquad{\boldsymbol{y}}(0)=({\boldsymbol{x}}_{0},t_{0})}</annotation>
  </semantics>
</math>

SVG (9.926 KB / 3.249 KB) :

ModifyingAbove 𝒚 With dot times left-parenthesis s right-parenthesis equals 𝑮 times left-parenthesis 𝒚 times left-parenthesis s right-parenthesis right-parenthesis comma 𝒚 times left-parenthesis 0 right-parenthesis equals left-parenthesis 𝒙 0 comma t 0 right-parenthesis

SVG (MathML can be enabled via browser plugin) rendering

MathML (1.955 KB / 474 B) :

y ˙ ( s ) = G ( y ( s ) ) , y ( 0 ) = ( x 0 , t 0 ) {\displaystyle {\dot {\boldsymbol {y}}}(s)={\boldsymbol {G}}({\boldsymbol {y}}(s)),\qquad {\boldsymbol {y}}(0)=({\boldsymbol {x}}_{0},t_{0})}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\dot {\boldsymbol {y}}}(s)={\boldsymbol {G}}({\boldsymbol {y}}(s)),\qquad {\boldsymbol {y}}(0)=({\boldsymbol {x}}_{0},t_{0})}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <mover>
              <mi mathvariant="bold-italic">y</mi>
              <mo>&#x02D9;<!-- ˙ --></mo>
            </mover>
          </mrow>
        </mrow>
        <mo stretchy="false">(</mo>
        <mi>s</mi>
        <mo stretchy="false">)</mo>
        <mo>=</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">G</mi>
        </mrow>
        <mo stretchy="false">(</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">y</mi>
        </mrow>
        <mo stretchy="false">(</mo>
        <mi>s</mi>
        <mo stretchy="false">)</mo>
        <mo stretchy="false">)</mo>
        <mo>,</mo>
        <mspace width="2em" />
        <mrow class="MJX-TeXAtom-ORD">
          <mi mathvariant="bold-italic">y</mi>
        </mrow>
        <mo stretchy="false">(</mo>
        <mn>0</mn>
        <mo stretchy="false">)</mo>
        <mo>=</mo>
        <mo stretchy="false">(</mo>
        <msub>
          <mrow class="MJX-TeXAtom-ORD">
            <mi mathvariant="bold-italic">x</mi>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>0</mn>
          </mrow>
        </msub>
        <mo>,</mo>
        <msub>
          <mi>t</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mn>0</mn>
          </mrow>
        </msub>
        <mo stretchy="false">)</mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\dot {\boldsymbol {y}}}(s)={\boldsymbol {G}}({\boldsymbol {y}}(s)),\qquad {\boldsymbol {y}}(0)=({\boldsymbol {x}}_{0},t_{0})}</annotation>
  </semantics>
</math>

SVG (7.057 KB / 2.922 KB) :

{\displaystyle {\dot {\boldsymbol {y}}}(s)={\boldsymbol {G}}({\boldsymbol {y}}(s)),\qquad {\boldsymbol {y}}(0)=({\boldsymbol {x}}_{0},t_{0})}

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Similar pages

Calculated based on the variables occurring on the entire Flow (mathematics) page

Identifiers

MathML observations

0results

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

0 results