1.11.8 problem 8

Internal problem ID [329]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 8
Date solved : Tuesday, September 30, 2025 at 03:57:25 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y&=\cosh \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=diff(diff(y(x),x),x)-4*y(x) = cosh(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-2 x} \left (\left (x +8 c_2 -\frac {1}{4}\right ) {\mathrm e}^{4 x}-x +8 c_1 -\frac {1}{2}\right )}{8} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 38

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

\begin{align*} y(x)&\to \frac {1}{32} e^{-2 x} \left (-4 x+e^{4 x} (4 x-1+32 c_1)-1+32 c_2\right ) \end{align*}

✓ Sympy. Time used: 0.063 (sec). Leaf size: 24

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

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