39.5.10 problem Problem 24.32

Internal problem ID [6552]
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 24.32
Date solved : Monday, January 27, 2025 at 02:12:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.383 (sec). Leaf size: 30

dsolve([diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=3*exp(-2*x),y(0) = 1, D(y)(0) = 1],y(x), singsol=all)
 

\[ y = \frac {3 \,{\mathrm e}^{-2 x}}{5}+\frac {{\mathrm e}^{-x} \left (4 \cos \left (2 x \right )+13 \sin \left (2 x \right )\right )}{10} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{10} e^{-2 x} \left (13 e^x \sin (2 x)+4 e^x \cos (2 x)+6\right ) \]