Internal problem ID [3101]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 353.
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^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 19
dsolve(x*(x^2+1)*diff(y(x),x) = a*x^2+y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (a \arcsinh \relax (x )+c_{1}\right ) x}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 33
DSolve[x(1+x^2)y'[x]==a x^2+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \left (a \tanh ^{-1}\left (\frac {x}{\sqrt {x^2+1}}\right )+c_1\right )}{\sqrt {x^2+1}} \\ \end{align*}