58.11.32 problem 32

Internal problem ID [14763]
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 : 32
Date solved : Thursday, October 02, 2025 at 09:50:54 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-10 y^{\prime }+29 y&=8 \,{\mathrm e}^{5 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=8 \\ \end{align*}

✓ Maple. Time used: 0.046 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)-10*diff(y(x),x)+29*y(x) = 8*exp(5*x); 
ic:=[y(0) = 0, D(y)(0) = 8]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -2 \,{\mathrm e}^{5 x} \left (-1-2 \sin \left (2 x \right )+\cos \left (2 x \right )\right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 24

ode=D[y[x],{x,2}]-10*D[y[x],x]+29*y[x]==8*Exp[5*x]; 
ic={y[0]==0,Derivative[1][y][0] ==8}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -2 e^{5 x} (-2 \sin (2 x)+\cos (2 x)-1) \end{align*}

✓ Sympy. Time used: 0.153 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(29*y(x) - 8*exp(5*x) - 10*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 8} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (4 \sin {\left (2 x \right )} - 2 \cos {\left (2 x \right )} + 2\right ) e^{5 x} \]