88.9.3 problem 3

Internal problem ID [24023]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 48
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:54:30 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y&=2 \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 12

ode:=diff(y(x),x)-y(x) = 2*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (2 x +c_1 \right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 15

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

\begin{align*} y(x)&\to e^x (2 x+c_1) \end{align*}

✓ Sympy. Time used: 0.071 (sec). Leaf size: 10

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

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