29.13.5 problem 359

Internal problem ID [4959]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 13
Problem number : 359
Date solved : Monday, January 27, 2025 at 09:55:54 AM
CAS classification : [_linear]

\begin{align*} x \left (-x^{2}+1\right ) y^{\prime }&=a \,x^{3}+\left (-2 x^{2}+1\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(x*(-x^2+1)*diff(y(x),x) = a*x^3+(-2*x^2+1)*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

\[ y(x)\to x \left (a+c_1 \sqrt {1-x^2}\right ) \]