29.12.35 problem 354

Internal problem ID [4954]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 354
Date solved : Monday, January 27, 2025 at 09:55:45 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 49

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

\[ y \left (x \right ) = x \left (-\frac {a \ln \left (x +\sqrt {x^{2}-1}\right ) \sqrt {x^{2}-1}}{\left (x -1\right ) \left (x +1\right )}+\frac {c_{1}}{\sqrt {x -1}\, \sqrt {x +1}}\right ) \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 25

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

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