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')`]
\[ \boxed {2 x \cos \left (y\right ) \sin \left (y\right ) y^{\prime }-\sin \left (y\right )^{2}=4 x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
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 \left (x \right ) = \arcsin \left (\sqrt {-c_{1} x +4 x^{2}}\right ) y \left (x \right ) = -\arcsin \left (\sqrt {-c_{1} x +4 x^{2}}\right ) \end{align*}
✓ Solution by Mathematica
Time used: 6.406 (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 -\arcsin \left (2 \sqrt {x (x+2 c_1)}\right ) y(x)\to \arcsin \left (2 \sqrt {x (x+2 c_1)}\right ) \end{align*}