89.22.10 problem 10

Internal problem ID [24798]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Exercises at page 161
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:48:07 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=12 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to \frac {x^3}{2}+c_4 x-\frac {1}{4} c_1 \cos (2 x)-\frac {1}{4} c_2 \sin (2 x)+c_3 \end{align*}

✓ Sympy. Time used: 0.057 (sec). Leaf size: 26

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

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