85.58.2 problem 2

Internal problem ID [22840]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. C Exercises at page 200
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:15:38 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }-6 y^{\prime }-12 y&=\sinh \left (x \right )^{4} \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 59

ode:=diff(diff(diff(y(x),x),x),x)+4*diff(diff(y(x),x),x)-6*diff(y(x),x)-12*y(x) = sinh(x)^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {1}{32}+c_3 \,{\mathrm e}^{-\left (3+\sqrt {3}\right ) x}+c_2 \,{\mathrm e}^{\left (-3+\sqrt {3}\right ) x}+\frac {\left (5-11 x +968 c_1 \right ) {\mathrm e}^{2 x}}{968}+\frac {{\mathrm e}^{-4 x}}{192}-\frac {{\mathrm e}^{-2 x}}{32}+\frac {{\mathrm e}^{4 x}}{1472} \]

✓ Mathematica. Time used: 0.491 (sec). Leaf size: 92

ode=D[y[x],{x,3}]+4*D[y[x],{x,2}]-6*D[y[x],{x,1}]-12*y[x]==Sinh[x]^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{-4 x}}{192}-\frac {e^{-2 x}}{32}+\frac {e^{4 x}}{1472}-\frac {1}{176} e^{2 x} \log \left (e^{2 x}\right )+c_1 e^{-\left (\left (3+\sqrt {3}\right ) x\right )}+c_2 e^{\left (\sqrt {3}-3\right ) x}+\left (\frac {5}{968}+c_3\right ) e^{2 x}-\frac {1}{32} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*y(x) - sinh(x)**4 - 6*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out