Internal problem ID [4633]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+5 y-2 \,{\mathrm e}^{-2 x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.01 (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)
\[ y \relax (x ) = -{\mathrm e}^{-2 x} \left (\cos \relax (x )-2\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 16
DSolve[{y''[x]+4*y'[x]+5*y[x]==2*Exp[-2*x],{y[0]==1,y'[0]==-2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -e^{-2 x} (\cos (x)-2) \\ \end{align*}