28.2.17 problem 17

Internal problem ID [4460]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 17
Date solved : Sunday, March 30, 2025 at 03:23:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 38

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

\[ y = \frac {\left (\left (-x +4 c_1 \right ) \cos \left (x \right )+4 \sin \left (x \right ) c_2 \right ) {\mathrm e}^{-x}}{4}-\frac {{\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right )}{16} \]

✓ Mathematica. Time used: 0.184 (sec). Leaf size: 47

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

\[ y(x)\to \frac {1}{16} e^{-x} \left (\left (e^{2 x}+2+16 c_1\right ) \sin (x)-\left (e^{2 x}+4 (x-4 c_2)\right ) \cos (x)\right ) \]

✗ Sympy

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

NotImplementedError : The given ODE y(x) - sin(x)*cosh(x)/2 + Derivative(y(x), x) + Derivative(y(x), (x, 2))/2 cannot be solved by the factorable group method