89.22.11 problem 11

Internal problem ID [24799]
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 : 11
Date solved : Thursday, October 02, 2025 at 10:48:07 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }&=12 x -2 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+diff(diff(y(x),x),x) = 12*x-2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.059 (sec). Leaf size: 34

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

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

✓ Sympy. Time used: 0.051 (sec). Leaf size: 26

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

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