38.3.6 problem 6

Internal problem ID [6484]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Test Excercise 25. page 1093
Problem number : 6
Date solved : Monday, January 27, 2025 at 02:07:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=2 \,{\mathrm e}^{-2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 14

dsolve([diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=2*exp(-2*x),y(0) = 1, D(y)(0) = -2],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 16

DSolve[{D[y[x],{x,2}]+4*D[y[x],x]+5*y[x]==2*Exp[-2*x],{y[0]==1,Derivative[1][y][0] ==-2}},y[x],x,IncludeSingularSolutions -> True]
 

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