35.6.3 problem 3

Internal problem ID [6153]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 3
Date solved : Sunday, March 30, 2025 at 10:41:25 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=diff(diff(y(x),x),x)+diff(y(x),x)-2*y(x) = exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left ({\mathrm e}^{4 x}+4 \,{\mathrm e}^{3 x} c_2 +4 c_1 \right ) {\mathrm e}^{-2 x}}{4} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 29

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

\[ y(x)\to \frac {e^{2 x}}{4}+c_1 e^{-2 x}+c_2 e^x \]

✓ Sympy. Time used: 0.158 (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 = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{x} + \frac {e^{2 x}}{4} \]