81.11.6 problem 15-5

Internal problem ID [21630]
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 : 15-5
Date solved : Thursday, October 02, 2025 at 07:59:14 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

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

\[ y = {\mathrm e}^{2 x} c_2 +{\mathrm e}^{-x} c_1 +\frac {\cos \left (x \right )}{10}-\frac {3 \sin \left (x \right )}{10} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 33

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

\begin{align*} y(x)&\to c_1 e^{-x}+c_2 e^{2 x}+\frac {1}{10} (\cos (x)-3 \sin (x)) \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 26

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

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{2 x} - \frac {3 \sin {\left (x \right )}}{10} + \frac {\cos {\left (x \right )}}{10} \]