28.2.26 problem 26

Internal problem ID [4469]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 26
Date solved : Sunday, March 30, 2025 at 03:23:24 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\left (5\right )}+4 y^{\prime \prime \prime }&=7+x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 39

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+4*diff(diff(diff(y(x),x),x),x) = 7+x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{4}}{96}+\frac {7 x^{3}}{24}+\frac {c_3 \,x^{2}}{2}-\frac {\sin \left (2 x \right ) c_1}{8}+\frac {\cos \left (2 x \right ) c_2}{8}+c_4 x +c_5 \]

✓ Mathematica. Time used: 0.176 (sec). Leaf size: 52

ode=D[y[x],{x,5}]+4*D[y[x],{x,3}]==7+x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^4}{96}+\frac {7 x^3}{24}+c_5 x^2+c_4 x+\frac {1}{8} c_2 \cos (2 x)-\frac {1}{8} c_1 \sin (2 x)+c_3 \]

✓ Sympy. Time used: 0.104 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + 4*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 5)) - 7,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} \sin {\left (2 x \right )} + C_{5} \cos {\left (2 x \right )} + \frac {x^{4}}{96} + \frac {7 x^{3}}{24} \]