1.15 problem 6.2

Internal problem ID [3861]

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]

Solve \begin {gather*} \boxed {x \left (1-x^{2}\right ) y^{\prime }+\left (2 x^{2}-1\right ) y-a \,x^{3}=0} \end {gather*}

Solution by Maple

Time used: 0.015 (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)
 

\[ y \relax (x ) = x \sqrt {x -1}\, \sqrt {x +1}\, c_{1}+a x \]

Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 23

DSolve[x*(1-x^2)*y'[x]+(2*x^2-1)*y[x]==a*x^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x \left (a+c_1 \sqrt {1-x^2}\right ) \\ \end{align*}