89.22.12 problem 12

Internal problem ID [24800]
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 : 12
Date solved : Thursday, October 02, 2025 at 10:48:08 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: 0.001 (sec). Leaf size: 27

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);
 

\[ y = {\mathrm e}^{x} c_1 +x^{2}-2 x^{3}+{\mathrm e}^{-x} c_2 +c_3 x +c_4 \]

✓ Mathematica. Time used: 0.036 (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 e^x+c_2 e^{-x}+c_3 \end{align*}

✓ Sympy. Time used: 0.062 (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)
 

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