Internal problem ID [107]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {2 x \cos \relax (y) \sin \relax (y) y^{\prime }-4 x^{2}-\left (\sin ^{2}\relax (y)\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve(2*x*cos(y(x))*sin(y(x))*diff(y(x),x) = 4*x^2+sin(y(x))^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \arccos \left (\sqrt {-4 x^{2}+x c_{1}+1}\right ) \\ y \relax (x ) = \pi -\arccos \left (\sqrt {-4 x^{2}+x c_{1}+1}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.345 (sec). Leaf size: 41
DSolve[2*x*Cos[y[x]]*Sin[y[x]]*y'[x] == 4*x^2+Sin[y[x]]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\text {ArcSin}\left (2 \sqrt {x (x+2 c_1)}\right ) \\ y(x)\to \text {ArcSin}\left (2 \sqrt {x (x+2 c_1)}\right ) \\ \end{align*}