89.5.13 problem 13

Internal problem ID [24363]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:22:12 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.093 (sec). Leaf size: 12

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

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