Internal problem ID [7936]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 356.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {\left (x^{2} \cos \relax (y)+2 y \sin \relax (x )\right ) y^{\prime }+2 x \sin \relax (y)+y^{2} \cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.091 (sec). Leaf size: 19
dsolve((x^2*cos(y(x))+2*y(x)*sin(x))*diff(y(x),x)+2*x*sin(y(x))+y(x)^2*cos(x) = 0,y(x), singsol=all)
\[ y \relax (x )^{2} \sin \relax (x )+\sin \left (y \relax (x )\right ) x^{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.191 (sec). Leaf size: 21
DSolve[2*x*Sin[y[x]] + Cos[x]*y[x]^2 + (x^2*Cos[y[x]] + 2*Sin[x]*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2 \sin (y(x))+y(x)^2 \sin (x)=c_1,y(x)\right ] \]