16.1.7 problem 3(a)

Internal problem ID [3409]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 3(a)
Date solved : Tuesday, March 04, 2025 at 04:37:51 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 22

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

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

✓ Sympy. Time used: 0.233 (sec). Leaf size: 10

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

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