86.10.9 problem 9

Internal problem ID [23189]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 9. The operational method. Exercise 9b at page 134
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:24:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }-y&=7 \,{\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=2*diff(diff(y(x),x),x)-4*diff(y(x),x)-y(x) = 7*exp(5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {\left (2+\sqrt {6}\right ) x}{2}} c_2 +{\mathrm e}^{-\frac {\left (-2+\sqrt {6}\right ) x}{2}} c_1 +\frac {7 \,{\mathrm e}^{5 x}}{29} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 48

ode=2*D[y[x],{x,2}]-4*D[y[x],x]-y[x]==7*Exp[5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {7 e^{5 x}}{29}+c_1 e^{x-\sqrt {\frac {3}{2}} x}+c_2 e^{\left (1+\sqrt {\frac {3}{2}}\right ) x} \end{align*}

✓ Sympy. Time used: 0.131 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - 7*exp(5*x) - 4*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x \left (1 - \frac {\sqrt {6}}{2}\right )} + C_{2} e^{x \left (1 + \frac {\sqrt {6}}{2}\right )} + \frac {7 e^{5 x}}{29} \]