Internal problem ID [3517]
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]
\[ \boxed {y^{\prime } x^{2}-\left (a x +y b \right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(x^2*diff(y(x),x) = (a*x+b*y(x))*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {x \left (a -1\right )}{\left (a -1\right ) c_{1} x^{-a +1}-b} \]
✓ Solution by Mathematica
Time used: 0.174 (sec). Leaf size: 36
DSolve[x^2 y'[x]==(a x+b y[x])y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {(a-1) x^{a+1}}{b x^a-(a-1) c_1 x} \\ y(x)\to 0 \\ \end{align*}