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Math Help - Word Problem Integration

  1. #1
    Senior Member polymerase's Avatar
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    Word Problem Integration

    Let x be a function of t such that \frac{dx}{dt}=2\sin^2 t\cos^2 x. Suppose that x\left(\frac{\pi}{4}\right)=\arctan \left(\frac{1}{2}+\frac{\pi}{4}\right). Then x(0)=

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  2. #2
    Senior Member Peritus's Avatar
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    <br />
\begin{gathered}<br />
  \frac{{dx}}<br />
{{dt}} = 2\sin ^2 t\cos ^2 x \hfill \\<br />
   \hfill \\<br />
   \Leftrightarrow \frac{1}<br />
{{\cos ^2 }}dx = 2\sin ^2 tdt \hfill \\ <br />
\end{gathered}

    <br />
 \Leftrightarrow \tan x = t - \frac{1}<br />
{2}\sin 2t + C<br />

    <br />
x(t) = a\tan \left( {t - \frac{1}<br />
{2}\sin 2t} \right) + K<br />

    now apply the I.V. .....
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