25.1.16 problem 16

Internal problem ID [4228]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 16
Date solved : Tuesday, March 04, 2025 at 05:56:55 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 12

ode=x*D[y[x],x]==x*y[x]+y[x]; 
ic=y[1]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{x-1} x \]

✓ Sympy. Time used: 0.221 (sec). Leaf size: 10

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

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