89.15.15 problem 15

Internal problem ID [24649]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 9. Nonhomogeneous Equations: Undetermined coefficients. Oral Exercises at page 131
Problem number : 15
Date solved : Thursday, October 02, 2025 at 10:46:43 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.061 (sec). Leaf size: 47

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

\begin{align*} y(x)&\to -3 x^2+c_4 x+\frac {1}{2} e^{-\sqrt {2} x} \left (c_1 e^{2 \sqrt {2} x}+c_2\right )+c_3 \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 32

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

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