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 : Monday, January 27, 2025 at 02:09:33 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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