84.6.1 problem 3.7

Internal problem ID [22102]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 3. Classification of first-order differential equations. Supplementary problems
Problem number : 3.7
Date solved : Thursday, October 02, 2025 at 08:24:54 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);
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 22

ode=D[y[x],x]==x*y[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: 0.140 (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)
 

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