87.2.13 problem 15

Internal problem ID [23248]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 17
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:26:52 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: 0.021 (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: 0.016 (sec). Leaf size: 18

ode=D[y[x],x]==y[x]*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: 0.179 (sec). Leaf size: 15

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)
 

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