87.16.3 problem 3

Internal problem ID [23572]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 119
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:43:03 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=\cos \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) = cos(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.053 (sec). Leaf size: 34

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

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

✓ Sympy. Time used: 0.124 (sec). Leaf size: 26

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

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