Internal problem ID [2861]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 112.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }+x \left (\sin \left (2 y\right )-x^{2} \left (\cos ^{2}\relax (y)\right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 21
dsolve(diff(y(x),x)+x*(sin(2*y(x))-x^2*cos(y(x))^2) = 0,y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {{\mathrm e}^{-x^{2}} c_{1}}{2}+\frac {x^{2}}{2}-\frac {1}{2}\right ) \]
✓ Solution by Mathematica
Time used: 33.138 (sec). Leaf size: 125
DSolve[y'[x]+x(Sin[2 y[x]]-x^2 Cos[y[x]]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcTan}\left (\frac {1}{2} \left (x^2-8 c_1 e^{-x^2}-1\right )\right ) \\ y(x)\to \text {ArcTan}\left (\frac {1}{2} \left (x^2-8 c_1 e^{-x^2}-1\right )\right ) \\ y(x)\to -\frac {1}{2} i \left (\log \left (-4 i e^{-x^2}\right )-\log \left (4 i e^{-x^2}\right )\right ) \\ y(x)\to \frac {1}{2} i \left (\log \left (-4 i e^{-x^2}\right )-\log \left (4 i e^{-x^2}\right )\right ) \\ \end{align*}