35.6.7 problem 7

Internal problem ID [6157]
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 : 7
Date solved : Sunday, March 30, 2025 at 10:41:31 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-diff(y(x),x)-2*y(x) = 3*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 27

ode=D[y[x],{x,2}]-D[y[x],x]-2*y[x]==3*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{-x}+e^{2 x} \left (x-\frac {1}{3}+c_2\right ) \]

✓ Sympy. Time used: 0.207 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) - 3*exp(2*x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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