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 : Wednesday, March 05, 2025 at 12:38:48 AM
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*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 22

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-2*y(x) = exp(2*x); 
ic:=y(0) = 1, D(y)(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.243 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) - exp(2*x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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