28.2.16 problem 16

Internal problem ID [4459]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 16
Date solved : Tuesday, March 04, 2025 at 06:45:32 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 42

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

\[ y \left (x \right ) = \frac {\left (34 c_{1} -4 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{-x}\right ) \cos \left (2 x \right )}{34}+\left (c_{2} +\frac {{\mathrm e}^{x}}{34}-\frac {{\mathrm e}^{-x}}{34}\right ) \sin \left (2 x \right ) \]

✓ Mathematica. Time used: 0.121 (sec). Leaf size: 46

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

\[ y(x)\to \frac {1}{34} (-(4-i) \cos ((2+i) x)-(4+i) \cosh ((1+2 i) x)+34 c_1 \cos (2 x)+34 c_2 \sin (2 x)) \]

✓ Sympy. Time used: 0.146 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = \left (C_{1} - \frac {4 \cosh {\left (x \right )}}{17}\right ) \cos {\left (2 x \right )} + \left (C_{2} + \frac {\sinh {\left (x \right )}}{17}\right ) \sin {\left (2 x \right )} \]