Internal problem ID [3008]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 260.
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 (x +a y\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x) = (x+a*y(x))*y(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{a \ln \relax (x )-c_{1}} \]
✓ Solution by Mathematica
Time used: 0.151 (sec). Leaf size: 22
DSolve[x^2 y'[x]==(x+a y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{-a \log (x)+c_1} \\ y(x)\to 0 \\ \end{align*}