86.10.8 problem 8

Internal problem ID [23188]
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 : 8
Date solved : Thursday, October 02, 2025 at 09:24:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

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

\[ y = {\mathrm e}^{\frac {\left (7+\sqrt {41}\right ) x}{2}} c_2 +{\mathrm e}^{-\frac {\left (-7+\sqrt {41}\right ) x}{2}} c_1 -\frac {{\mathrm e}^{2 x}}{8} \]

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 49

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

\begin{align*} y(x)&\to -\frac {e^{2 x}}{8}+c_1 e^{-\frac {1}{2} \left (\sqrt {41}-7\right ) x}+c_2 e^{\frac {1}{2} \left (7+\sqrt {41}\right ) x} \end{align*}

✓ Sympy. Time used: 0.133 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (7 - \sqrt {41}\right )}{2}} + C_{2} e^{\frac {x \left (\sqrt {41} + 7\right )}{2}} - \frac {e^{2 x}}{8} \]