1.6 problem 6

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*}