50.14.19 problem 3(c)

Internal problem ID [8057]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 3(c)
Date solved : Sunday, March 30, 2025 at 12:41:43 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: 0.004 (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: 0.048 (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]
 

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

✓ Sympy. Time used: 0.188 (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)
 

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