89.23.10 problem 10

Internal problem ID [24814]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Miscellaneous Exercises at page 162
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:48:15 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=24 \,{\mathrm e}^{2 x} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+13*y(x) = 24*exp(2*x)*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \left (c_2 \sin \left (3 x \right )+c_1 \cos \left (3 x \right )+3 \sin \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 30

ode=D[y[x],{x,2}]-4*D[y[x],{x,1}]+13*y[x]==24*Exp[2*x]*Sin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{2 x} (3 \sin (x)+c_2 \cos (3 x)+c_1 \sin (3 x)) \end{align*}

✓ Sympy. Time used: 0.173 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(13*y(x) - 24*exp(2*x)*sin(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (3 x \right )} + C_{2} \cos {\left (3 x \right )} + 3 \sin {\left (x \right )}\right ) e^{2 x} \]