58.11.7 problem 7

Internal problem ID [14738]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:50:39 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+5 y&=2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

ode:=diff(diff(y(x),x),x)+6*diff(y(x),x)+5*y(x) = 2*exp(x)+10*exp(5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (\cosh \left (2 x \right ) {\mathrm e}^{8 x}+3 c_1 \,{\mathrm e}^{4 x}+3 c_2 \right ) {\mathrm e}^{-5 x}}{3} \]

✓ Mathematica. Time used: 0.134 (sec). Leaf size: 36

ode=D[y[x],{x,2}]+6*D[y[x],x]+5*y[x]==2*Exp[x]+10*Exp[5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{6} e^x \left (e^{4 x}+1\right )+c_1 e^{-5 x}+c_2 e^{-x} \end{align*}

✓ Sympy. Time used: 0.133 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 10*exp(5*x) - 2*exp(x) + 6*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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