85.1.2 problem 1 (b)

Internal problem ID [22407]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 1 (b)
Date solved : Thursday, October 02, 2025 at 08:38:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }-5 y&={\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)-5*y(x) = exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} c_2 +{\mathrm e}^{5 x} c_1 -\frac {{\mathrm e}^{3 x}}{8} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 31

ode=D[y[x],{x,2}]-4*D[y[x],x]-5*y[x]==Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {e^{3 x}}{8}+c_1 e^{-x}+c_2 e^{5 x} \end{align*}

✓ Sympy. Time used: 0.108 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) - exp(3*x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{5 x} - \frac {e^{3 x}}{8} \]