71.4.1 problem 1

Internal problem ID [14302]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 1
Date solved : Monday, March 31, 2025 at 12:16:16 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {3 y}{\left (x -5\right ) \left (x +3\right )}+{\mathrm e}^{-x} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 34

ode:=diff(y(x),x) = 3*y(x)/(x-5)/(x+3)+exp(-x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (\int \frac {{\mathrm e}^{-x} \left (x +3\right )^{{3}/{8}}}{\left (x -5\right )^{{3}/{8}}}d x +c_1 \right ) \left (x -5\right )^{{3}/{8}}}{\left (x +3\right )^{{3}/{8}}} \]

✓ Mathematica. Time used: 0.104 (sec). Leaf size: 70

ode=D[y[x],x]==3*y[x]/( (x-5)*(x+3))+Exp[-x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \exp \left (\int _1^x\frac {3}{K[1]^2-2 K[1]-15}dK[1]\right ) \left (\int _1^x\exp \left (-K[2]-\int _1^{K[2]}\frac {3}{K[1]^2-2 K[1]-15}dK[1]\right )dK[2]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - exp(-x) - 3*y(x)/((x - 5)*(x + 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out