81.6.5 problem 7-5

Internal problem ID [21551]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 7. Linear Differential Equations. Page 101.
Problem number : 7-5
Date solved : Thursday, October 02, 2025 at 07:47:58 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 10

ode:=diff(y(x),x) = exp(x)+y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x +c_1 \right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 13

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

\begin{align*} y(x)&\to e^x (x+c_1) \end{align*}

✓ Sympy. Time used: 0.074 (sec). Leaf size: 8

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

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