66.2.24 problem Problem 33

Internal problem ID [13852]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 33
Date solved : Monday, March 31, 2025 at 08:15:14 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 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)+2*diff(y(x),x)+y(x) = sinh(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-x^{2}+\left (4 c_1 +1\right ) x +4 c_2 \right ) {\mathrm e}^{-x}}{4}+\frac {\cosh \left (x \right )}{4} \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{8} e^{-x} \left (-2 x^2+e^{2 x}+8 c_2 x+8 c_1\right ) \]

✗ Sympy

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