8.11.27 problem 50

Internal problem ID [895]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 50
Date solved : Tuesday, March 04, 2025 at 11:59:52 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 30

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

\[ y = \frac {{\mathrm e}^{2 x} \left (4 x +32 c_2 -1\right )}{32}+\frac {{\mathrm e}^{-2 x} \left (x +8 c_1 \right )}{8} \]

✓ Mathematica. Time used: 0.032 (sec). Leaf size: 38

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

\[ y(x)\to \frac {1}{32} e^{-2 x} \left (4 x+e^{4 x} (4 x-1+32 c_1)+1+32 c_2\right ) \]

✓ Sympy. Time used: 0.110 (sec). Leaf size: 24

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

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