Internal problem ID [4657]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }-2 y-\sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-x} c_{1}+\frac {\cos \left (2 x \right )}{20}-\frac {3 \sin \left (2 x \right )}{20} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 37
DSolve[y''[x]-y'[x]-2*y[x]==Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x}+c_2 e^{2 x}+\frac {1}{20} (\cos (2 x)-3 \sin (2 x)) \\ \end{align*}