86.7.11 problem 13

Internal problem ID [23158]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5c at page 83
Problem number : 13
Date solved : Thursday, October 02, 2025 at 09:23:35 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-9 y^{\prime }+14 y&={\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)-9*diff(y(x),x)+14*y(x) = exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 32

ode=D[y[x],{x,2}]-9*D[y[x],x]+14*y[x]==Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{25} e^{2 x} \left (-5 x+25 c_2 e^{5 x}-1+25 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.133 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(14*y(x) - exp(2*x) - 9*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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