Internal problem ID [3002]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 254.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-y \left (b x +a \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 16
dsolve(x^2*diff(y(x),x) = (b*x+a)*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {a}{x}} x^{b} \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 24
DSolve[x^2 y'[x]==(a+b x)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-\frac {a}{x}} x^b \\ y(x)\to 0 \\ \end{align*}