51.1.6 problem 6

Internal problem ID [10276]
Book : First order enumerated odes
Section : section 1
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 07:16:27 PM
CAS classification : [_separable]

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

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

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

\[ y = c_1 \,{\mathrm e}^{\frac {a \,x^{2}}{2}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 23

ode=D[y[x],x]==a*x*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{\frac {a x^2}{2}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.153 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a*x*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {a x^{2}}{2}} \]