Internal problem ID [6569]
Book: First order enumerated odes
Section: section 1
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-a x y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 13
dsolve(diff(y(x),x)=a*x*y(x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {a \,x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 23
DSolve[y'[x]==a*x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {a x^2}{2}} \\ y(x)\to 0 \\ \end{align*}