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Display information for equation id:math.1508.25 on revision:1508
* Page found: Lagrangegleichungen 2. Art (eq math.1508.25)
(force rerendering)Occurrences on the following pages:
Hash: e5a230d2b693007fe994fdedcd856d4a
TeX (original user input):
\begin{align}
& \frac{{\dot{\omega }}}{\omega }=\frac{2c}{{{R}_{o}}-ct} \\
& \int{\frac{d\omega }{\omega }=2c\int{\frac{dt}{{{R}_{o}}-ct}}} \\
& \ln \omega =-2\ln ({{R}_{o}}-ct)+const \\
& \ln \omega =\ln \frac{con\tilde{s}}{{{({{R}_{o}}-ct)}^{2}}} \\
& \omega =\frac{con\tilde{s}}{{{({{R}_{o}}-ct)}^{2}}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{\frac {\dot {\omega }}{\omega }}={\frac {2c}{{{R}_{o}}-ct}}\\&\int {{\frac {d\omega }{\omega }}=2c\int {\frac {dt}{{{R}_{o}}-ct}}}\\&\ln \omega =-2\ln({{R}_{o}}-ct)+const\\&\ln \omega =\ln {\frac {con{\tilde {s}}}{{({{R}_{o}}-ct)}^{2}}}\\&\omega ={\frac {con{\tilde {s}}}{{({{R}_{o}}-ct)}^{2}}}\\\end{aligned}}
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MathML (3.33 KB / 487 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>ω</mi><mo>˙</mo></mover></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>ω</mi></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>c</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo>−</mo><mi>c</mi><mi>t</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>ω</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>ω</mi></mrow></mfrac></mrow><mo>=</mo><mn>2</mn><mi>c</mi><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>t</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo>−</mo><mi>c</mi><mi>t</mi></mrow></mrow></mfrac></mrow></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>ln</mi><mo>⁡</mo><mi>ω</mi><mo>=</mo><mo>−</mo><mn>2</mn><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo>−</mo><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi>t</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi>ln</mi><mo>⁡</mo><mi>ω</mi><mo>=</mo><mi>ln</mi><mo>⁡</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>c</mi><mi>o</mi><mi>n</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>s</mi><mo>~</mo></mover></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo>−</mo><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mi>ω</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>c</mi><mi>o</mi><mi>n</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>s</mi><mo>~</mo></mover></mrow></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><msub><mi>R</mi><mrow data-mjx-texclass="ORD"><mi>o</mi></mrow></msub><mo>−</mo><mi>c</mi><mi>t</mi><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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