Internal problem ID [7755]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 175.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+x^{3} a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x*(x^2-1)*diff(y(x),x) - (2*x^2-1)*y(x) + a*x^3=0,y(x), singsol=all)
\[ y \relax (x ) = x \sqrt {x -1}\, \sqrt {x +1}\, c_{1}+a x \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 23
DSolve[x*(x^2-1)*y'[x] - (2*x^2-1)*y[x] + a*x^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (a+c_1 \sqrt {1-x^2}\right ) \\ \end{align*}