65.11.2 problem 2

Internal problem ID [15798]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.4, page 218
Problem number : 2
Date solved : Thursday, October 02, 2025 at 10:28:08 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 48

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+4*diff(diff(y(x),x),x) = 24*x^2-6*x+14+32*cos(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-c_1 -10\right ) \cos \left (2 x \right )}{4}+\frac {\left (-8 x -c_2 \right ) \sin \left (2 x \right )}{4}+\frac {x^{4}}{2}-\frac {x^{3}}{4}+\frac {x^{2}}{4}+c_3 x +c_4 \]

✓ Mathematica. Time used: 60.131 (sec). Leaf size: 123

ode=D[y[x],{x,4}]+4*D[y[x],{x,2}]==24*x^2-6*x+14+32*Cos[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x\int _1^{K[4]}\left (c_1 \cos (2 K[3])+\int _1^{K[3]}-\left (\left (12 K[1]^2-3 K[1]+16 \cos (2 K[1])+7\right ) \sin (2 K[1])\right )dK[1] \cos (2 K[3])+c_2 \sin (2 K[3])+\sin (2 K[3]) \int _1^{K[3]}\cos (2 K[2]) \left (12 K[2]^2-3 K[2]+16 \cos (2 K[2])+7\right )dK[2]\right )dK[3]dK[4]+c_4 x+c_3 \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-24*x**2 + 6*x - 32*cos(2*x) + 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)) - 14,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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