Internal problem ID [4180]
Book: A treatise on ordinary and partial differential equations by William Woolsey Johnson.
1913
Section: Chapter 2, Equations of the first order and degree. page 20
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-a x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve(diff(y(x),x)=a*y(x)^2*x,y(x), singsol=all)
\[ y \relax (x ) = \frac {2}{-a \,x^{2}+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 24
DSolve[y'[x]==a*y[x]^2*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{a x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}