35.6.8 problem 8

Internal problem ID [6158]
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 : 8
Date solved : Sunday, March 30, 2025 at 10:41:33 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-16 y&=40 \,{\mathrm e}^{4 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-16*y(x) = 40*exp(4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-4 x} c_1 +{\mathrm e}^{4 x} \left (c_2 +5 x \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 29

ode=D[y[x],{x,2}]-16*y[x]==40*Exp[4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{4 x} \left (5 x-\frac {5}{8}+c_1\right )+c_2 e^{-4 x} \]

✓ Sympy. Time used: 0.113 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-16*y(x) - 40*exp(4*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{- 4 x} + \left (C_{1} + 5 x\right ) e^{4 x} \]