88.23.15 problem 17

Internal problem ID [24189]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Miscellaneous Exercises at page 162
Problem number : 17
Date solved : Thursday, October 02, 2025 at 10:00:37 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

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

\[ y = {\mathrm e}^{\frac {\left (\sqrt {5}+1\right ) x}{2}} c_2 +{\mathrm e}^{-\frac {\left (\sqrt {5}-1\right ) x}{2}} c_1 -\cosh \left (x \right ) \]

✓ Mathematica. Time used: 0.135 (sec). Leaf size: 40

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

\begin{align*} y(x)&\to -\cosh (x)+e^{-\frac {1}{2} \left (\sqrt {5}-1\right ) x} \left (c_2 e^{\sqrt {5} x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.176 (sec). Leaf size: 32

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

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