57.1.6 problem 6

Internal problem ID [8990]
Book : First order enumerated odes
Section : section 1
Problem number : 6
Date solved : Monday, January 27, 2025 at 05:26:36 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=a x y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

dsolve(diff(y(x),x)=a*x*y(x),y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {a \,x^{2}}{2}} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 23

DSolve[D[y[x],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*}