84.23.6 problem 14.6

Internal problem ID [22250]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 14. The method of undetermined coefficients. Solved problems. Page 71
Problem number : 14.6
Date solved : Thursday, October 02, 2025 at 08:36:36 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-5 y&=2 \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x)-5*y(x) = 2*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{x}}{2}+{\mathrm e}^{5 x} c_1 \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 21

ode=D[y[x],x]-5*y[x]==2*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {e^x}{2}+c_1 e^{5 x} \end{align*}

✓ Sympy. Time used: 0.079 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) - 2*exp(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} e^{4 x} - \frac {1}{2}\right ) e^{x} \]