Internal problem ID [3370]
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')`]
\[ \boxed {y^{\prime }+x \left (\sin \left (2 y\right )-x^{2} \cos \left (y\right )^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \arctan \left (\frac {c_{1} {\mathrm e}^{-x^{2}}}{2}+\frac {x^{2}}{2}-\frac {1}{2}\right ) \]
✓ Solution by Mathematica
Time used: 21.108 (sec). Leaf size: 105
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 \arctan \left (\frac {1}{2} \left (x^2-8 c_1 e^{-x^2}-1\right )\right ) y(x)\to -\arctan \left (-\frac {x^2}{2}+4 c_1 e^{-x^2}+\frac {1}{2}\right ) y(x)\to -\frac {1}{2} \pi e^{x^2} \sqrt {e^{-2 x^2}} y(x)\to \frac {1}{2} \pi e^{x^2} \sqrt {e^{-2 x^2}} \end{align*}