81.11.18 problem 15-17

Internal problem ID [21642]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 15. Method of undetermined coefficients. Page 337.
Problem number : 15-17
Date solved : Thursday, October 02, 2025 at 07:59:22 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 5 y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to \frac {1}{3} e^{-x} (\sin (x)+3 c_2 \cos (2 x)+3 c_1 \sin (2 x)) \end{align*}

✓ Sympy. Time used: 0.172 (sec). Leaf size: 24

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

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