Internal problem ID [10575]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, section 1.3. Exercises page 22
Problem number: 6(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-x^{2} \sin \left (y\right )=0} \] With initial conditions \begin {align*} [y \left (1\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 2.719 (sec). Leaf size: 97
dsolve([diff(y(x),x)=x^2*sin(y(x)),y(1) = -2],y(x), singsol=all)
\[ y \left (x \right ) = \arctan \left (\frac {2 \sin \left (2\right ) {\mathrm e}^{\frac {\left (x -1\right ) \left (x^{2}+x +1\right )}{3}}}{\left (-1+\cos \left (2\right )\right ) {\mathrm e}^{\frac {2 \left (x -1\right ) \left (x^{2}+x +1\right )}{3}}-\cos \left (2\right )-1}, \frac {\left (-\cos \left (2\right )+1\right ) {\mathrm e}^{\frac {2 \left (x -1\right ) \left (x^{2}+x +1\right )}{3}}-\cos \left (2\right )-1}{\left (-1+\cos \left (2\right )\right ) {\mathrm e}^{\frac {2 \left (x -1\right ) \left (x^{2}+x +1\right )}{3}}-\cos \left (2\right )-1}\right ) \]
✓ Solution by Mathematica
Time used: 6.739 (sec). Leaf size: 24
DSolve[{y'[x]==x^2*Sin[y[x]],{y[1]==-2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 \cot ^{-1}\left (e^{\frac {1}{3}-\frac {x^3}{3}} \cot (1)\right ) \\ \end{align*}