Internal problem ID [4369]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 6.2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y=a \,x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x*(1-x^2)*diff(y(x),x)+(2*x^2-1)*y(x)=a*x^3,y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {x -1}\, x \sqrt {x +1}\, c_{1} +a x \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 23
DSolve[x*(1-x^2)*y'[x]+(2*x^2-1)*y[x]==a*x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \left (a+c_1 \sqrt {1-x^2}\right ) \]