Internal problem ID [4698]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page
248
Problem number: Problem 24.29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }-3 y-\sin \left (2 x \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 27
dsolve([diff(y(x),x$2)+2*diff(y(x),x)-3*y(x)=sin(2*x),y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = -\frac {4 \,{\mathrm e}^{-3 x} \left (\left (\cos \left (2 x \right )+\frac {7 \sin \left (2 x \right )}{4}\right ) {\mathrm e}^{3 x}-\frac {13 \,{\mathrm e}^{4 x}}{8}+\frac {5}{8}\right )}{65} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 36
DSolve[{y''[x]-2*y'[x]-3*y[x]==Sin[2*x],{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{130} \left (-13 e^{-x}+5 e^{3 x}-14 \sin (2 x)+8 \cos (2 x)\right ) \\ \end{align*}