78.23.5 problem 3 (e)

Internal problem ID [18456]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 9. Laplace transforms. Section 50. Applications to differential equations. Problems at page 462
Problem number : 3 (e)
Date solved : Tuesday, January 28, 2025 at 11:50:20 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \,{\mathrm e}^{-x} \sin \left (x \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.266 (sec). Leaf size: 16

dsolve([diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=3*exp(-x)*sin(x),y(0) = 0, D(y)(0) = 3],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} \left (\sin \left (x \right )+\sin \left (2 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 18

DSolve[{D[y[x],{x,2}]+2*D[y[x],x]+5*y[x]==3*Exp[-x]*Sin[x],{y[0]==0,Derivative[1][y][0] == 3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} (\sin (x)+\sin (2 x)) \]