Internal problem ID [3100]
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]
\[ \boxed {x \left (x^{2}+1\right ) y^{\prime }-x^{2} a -y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x*(x^2+1)*diff(y(x),x) = a*x^2+y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (a \,\operatorname {arcsinh}\left (x \right )+c_{1} \right ) x}{\sqrt {x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 23
DSolve[x(1+x^2)y'[x]==a x^2+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x (a \text {arcsinh}(x)+c_1)}{\sqrt {x^2+1}} \\ \end{align*}