Internal problem ID [3103]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 355.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x \left (x^{2}+1\right ) y^{\prime }-a \,x^{3}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(x*(x^2+1)*diff(y(x),x) = a*x^3+y(x),y(x), singsol=all)
\[ y \relax (x ) = a x +\frac {x c_{1}}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 21
DSolve[x(1+x^2)y'[x]==a x^3+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (a+\frac {c_1}{\sqrt {x^2+1}}\right ) \\ \end{align*}