Internal problem ID [3615]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 359.
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*(-x^2+1)*diff(y(x),x) = a*x^3+(-2*x^2+1)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {x -1}\, x \sqrt {x +1}\, c_{1} +a x \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 23
DSolve[x(1-x^2)y'[x]==a x^3+(1-2 x^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \left (a+c_1 \sqrt {1-x^2}\right ) \]