Internal problem ID [3009]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 261.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-\left (a x +b y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 33
dsolve(x^2*diff(y(x),x) = (a*x+b*y(x))*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (a -1\right )}{x^{-a} c_{1} x a -x^{-a} c_{1} x -b} \]
✓ Solution by Mathematica
Time used: 0.167 (sec). Leaf size: 31
DSolve[x^2 y'[x]==(a x+b y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\frac {b}{x-a x}+c_1 x^{-a}} \\ y(x)\to 0 \\ \end{align*}