39.1.3 problem Problem 11.3

Internal problem ID [6508]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number : Problem 11.3
Date solved : Wednesday, March 05, 2025 at 12:53:54 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

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

\[ y = c_2 \,{\mathrm e}^{-x}+{\mathrm e}^{2 x} c_1 +\frac {\cos \left (2 x \right )}{20}-\frac {3 \sin \left (2 x \right )}{20} \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 37

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

\[ y(x)\to c_1 e^{-x}+c_2 e^{2 x}+\frac {1}{20} (\cos (2 x)-3 \sin (2 x)) \]

✓ Sympy. Time used: 0.215 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{2 x} - \frac {3 \sin {\left (2 x \right )}}{20} + \frac {\cos {\left (2 x \right )}}{20} \]