39.5.7 problem Problem 24.29

Internal problem ID [6549]
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
Date solved : Monday, January 27, 2025 at 02:12:07 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 x \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.185 (sec). Leaf size: 34

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)
 

\[ y = -\frac {4 \,{\mathrm e}^{-3 x} \left (\left (\cos \left (2 x \right )+\frac {7 \sin \left (2 x \right )}{4}\right ) {\mathrm e}^{3 x}-\frac {13 \,{\mathrm e}^{4 x}}{8}+\frac {5}{8}\right )}{65} \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 36

DSolve[{D[y[x],{x,2}]-2*D[y[x],x]-3*y[x]==Sin[2*x],{y[0]==0,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{130} \left (-13 e^{-x}+5 e^{3 x}-14 \sin (2 x)+8 \cos (2 x)\right ) \]