67.15.73 problem 22.14 (d)

Internal problem ID [16791]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.14 (d)
Date solved : Thursday, October 02, 2025 at 01:38:53 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=20 \sinh \left (x \right ) \end{align*}

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

ode:=diff(diff(y(x),x),x)-4*diff(y(x),x)+5*y(x) = 20*sinh(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \sin \left (x \right ) c_2 +{\mathrm e}^{2 x} \cos \left (x \right ) c_1 +5 \,{\mathrm e}^{x}-{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 1.067 (sec). Leaf size: 101

ode=D[y[x],{x,2}]-4*D[y[x],x]+5*y[x]==20*Sinh[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 \left (5 \left (1-i \tan \left (\frac {x}{2}\right )\right )^{2 i}-\left (1+i \tan \left (\frac {x}{2}\right )\right )^{2 i}\right ) \sinh (x)}{\left (1-i \tan \left (\frac {x}{2}\right )\right )^{2 i}-\left (1+i \tan \left (\frac {x}{2}\right )\right )^{2 i}}+e^{2 x} (c_2 \cos (x)+c_1 \sin (x)) \end{align*}

✓ Sympy. Time used: 0.191 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 20*sinh(x) - 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )}\right ) e^{2 x} + 6 \sinh {\left (x \right )} + 4 \cosh {\left (x \right )} \]