86.10.5 problem 5

Internal problem ID [23185]
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 : 5
Date solved : Thursday, October 02, 2025 at 09:24:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-11 y^{\prime }+30 y&={\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)-11*diff(y(x),x)+30*y(x) = exp(5*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 24

ode=D[y[x],{x,2}]-11*D[y[x],x]+30*y[x]==Exp[5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.127 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(30*y(x) - exp(5*x) - 11*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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