38.4.4 problem 4

Internal problem ID [6490]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 25. Second order differential equations. Further problems 25. page 1094
Problem number : 4
Date solved : Wednesday, March 05, 2025 at 12:52:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 32

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

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

✓ Mathematica. Time used: 0.057 (sec). Leaf size: 31

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 4*sinh(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)/2 - 2*sinh(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2))/2 cannot be solved by the factorable group method