23.5.45 problem 45

Internal problem ID [6654]
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 : 45
Date solved : Tuesday, September 30, 2025 at 03:50:33 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} -3 y-y^{\prime }+3 y^{\prime \prime }+y^{\prime \prime \prime }&=\cosh \left (x \right ) \end{align*}

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

ode:=-3*y(x)-diff(y(x),x)+3*diff(diff(y(x),x),x)+diff(diff(diff(y(x),x),x),x) = cosh(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-8 x +64 c_3 -4\right ) {\mathrm e}^{-x}}{64}+c_2 \,{\mathrm e}^{-3 x}+\frac {{\mathrm e}^{x} \left (x +16 c_1 -\frac {3}{4}\right )}{16} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 43

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

\begin{align*} y(x)&\to c_1 e^{-3 x}+e^{-x} \left (-\frac {x}{8}+c_2\right )+e^x \left (\frac {x}{16}-\frac {3}{64}+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.150 (sec). Leaf size: 34

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

\[ y{\left (x \right )} = C_{1} e^{- 3 x} + C_{2} e^{- x} + C_{3} e^{x} + \frac {3 x \sinh {\left (x \right )}}{16} - \frac {x \cosh {\left (x \right )}}{16} \]