37.1.7 problem 10.2.11 (i)

Internal problem ID [6394]
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)
Date solved : Monday, January 27, 2025 at 02:00:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.011 (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)
 

\[ y = \frac {\left (2+3 x \right ) {\mathrm e}^{2 x}}{9}+\frac {7 \,{\mathrm e}^{-x}}{9} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{9} e^{-x} \left (e^{3 x} (3 x+2)+7\right ) \]