Internal problem ID [2822]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 67.
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: 0.0 (sec). Leaf size: 18
dsolve(diff(y(x),x) = a*x*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {2}{-a \,x^{2}+2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.139 (sec). Leaf size: 24
DSolve[y'[x]==a x y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{a x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}