Internal problem ID [2903]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 155.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x -a \,x^{2}-b y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x*diff(y(x),x) = a*x^2+b*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {a \,x^{2}}{b -2}+x^{b} c_{1} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 24
DSolve[x y'[x]==a x^2+b y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {a x^2}{2-b}+c_1 x^b \\ \end{align*}