23.5.35 problem 35

Internal problem ID [6644]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 35
Date solved : Tuesday, September 30, 2025 at 03:50:28 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 35

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

\[ y = \frac {\left (-6 x +72 c_2 -2\right ) {\mathrm e}^{-x}}{72}+c_3 \,{\mathrm e}^{2 x}-\frac {{\mathrm e}^{x} \left (x -4 c_1 +\frac {1}{2}\right )}{4} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 48

ode=2*y[x] - D[y[x],x] - 2*D[y[x],{x,2}] + D[y[x],{x,3}] == Sinh[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{72} e^{-x} \left (-6 x-9 e^{2 x} (2 x+1-8 c_2)+72 c_3 e^{3 x}-5+72 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.212 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - sinh(x) - Derivative(y(x), x) - 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{x} + C_{3} e^{2 x} - \frac {x \sinh {\left (x \right )}}{6} - \frac {x \cosh {\left (x \right )}}{3} \]