Internal problem ID [2887]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 139.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {2 y^{\prime }-2 \left (\sin ^{2}\relax (y)\right ) \tan \relax (y)+x \sin \left (2 y\right )=0} \end {gather*}
✗ Solution by Maple
dsolve(2*diff(y(x),x) = 2*sin(y(x))^2*tan(y(x))-x*sin(2*y(x)),y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 60.359 (sec). Leaf size: 61
DSolve[2 y'[x]==2 Sin[y[x]]^2 Tan[y[x]]- x Sin[2 y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {Erf}(x)+4 c_1\right )}\right ) \\ y(x)\to \cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {Erf}(x)+4 c_1\right )}\right ) \\ \end{align*}