Internal problem ID [4543]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.2, ODEs with constant Coefficients. page
307
Problem number: 10.2.11 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-y^{\prime }-2 y-{\mathrm e}^{2 x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 22
dsolve([diff(y(x),x$2)-diff(y(x),x)-2*y(x)=exp(2*x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (3 x +2\right ) {\mathrm e}^{2 x}}{9}+\frac {7 \,{\mathrm e}^{-x}}{9} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 27
DSolve[{y''[x]-y'[x]-2*y[x]==Exp[2*x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} e^{-x} \left (e^{3 x} (3 x+2)+7\right ) \\ \end{align*}