84.9.4 problem 5.5 and 5.6

Internal problem ID [22127]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 5. Homogeneous differential equations. Solved problems. Page 19
Problem number : 5.5 and 5.6
Date solved : Thursday, October 02, 2025 at 08:25:51 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 15

ode:=diff(y(x),x) = x*y(x); 
ic:=[y(1) = -2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

ode=D[y[x],x]==(x^2*y[x]^2)/(x*y[x]); 
ic={y[1]==-2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -2 e^{\frac {1}{2} \left (x^2-1\right )} \end{align*}

✓ Sympy. Time used: 0.147 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x) + Derivative(y(x), x),0) 
ics = {y(1): -2} 
dsolve(ode,func=y(x),ics=ics)
 

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