Internal problem ID [7780]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 200.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (a \left (\sin ^{2}\relax (x )\right )+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \left (\sin ^{2}\relax (x )\right )+c \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 56
dsolve((a*sin(x)^2+b)*diff(y(x),x) + a*y(x)*sin(2*x) + A*x*(a*sin(x)^2+c)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {-2 A x a \sin \left (2 x \right )+2 A \,x^{2} a +4 c A \,x^{2}-A a \cos \left (2 x \right )-8 c_{1}}{4 a \cos \left (2 x \right )-4 a -8 b} \]
✓ Solution by Mathematica
Time used: 0.178 (sec). Leaf size: 55
DSolve[(a*Sin[x]^2+b)*y'[x] + a*y[x]*Sin[2*x] + A*x*(a*Sin[x]^2+c)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 A x^2 (a+2 c)-a A (2 x \sin (2 x)+\cos (2 x))+4 c_1}{4 a \cos (2 x)-4 (a+2 b)} \\ \end{align*}