64.2.9 problem 6(a)

Internal problem ID [13269]
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)
Date solved : Tuesday, January 28, 2025 at 05:13:40 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=x^{2} \sin \left (y\right ) \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 3.289 (sec). Leaf size: 97

dsolve([diff(y(x),x)=x^2*sin(y(x)),y(1) = -2],y(x), singsol=all)
 

\[ y = \arctan \left (\frac {2 \sin \left (2\right ) {\mathrm e}^{\frac {\left (x -1\right ) \left (x^{2}+x +1\right )}{3}}}{\left (-1+\cos \left (2\right )\right ) {\mathrm e}^{\frac {2 \left (x -1\right ) \left (x^{2}+x +1\right )}{3}}-\cos \left (2\right )-1}, \frac {\left (1-\cos \left (2\right )\right ) {\mathrm e}^{\frac {2 \left (x -1\right ) \left (x^{2}+x +1\right )}{3}}-\cos \left (2\right )-1}{\left (-1+\cos \left (2\right )\right ) {\mathrm e}^{\frac {2 \left (x -1\right ) \left (x^{2}+x +1\right )}{3}}-\cos \left (2\right )-1}\right ) \]

✓ Solution by Mathematica

Time used: 0.420 (sec). Leaf size: 23

DSolve[{D[y[x],x]==x^2*Sin[y[x]],{y[1]==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\arccos \left (\tanh \left (\text {arctanh}(\cos (2))-\frac {x^3}{3}+\frac {1}{3}\right )\right ) \]