Internal problem ID [4630]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+y-{\mathrm e}^{-2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=exp(-2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+x \,{\mathrm e}^{-x} c_{1}+{\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 24
DSolve[y''[x]+2*y'[x]+y[x]==Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-2 x} \left (1+e^x (c_2 x+c_1)\right ) \\ \end{align*}