67.15.57 problem 22.12 (b)

Internal problem ID [16775]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.12 (b)
Date solved : Thursday, October 02, 2025 at 01:38:45 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=10 \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 34

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x) = 10*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{4 x} c_1}{64}+\frac {c_2 \,x^{2}}{2}+\frac {\sin \left (2 x \right )}{8}-\frac {\cos \left (2 x \right )}{4}+c_3 x +c_4 \]

✓ Mathematica. Time used: 22.144 (sec). Leaf size: 71

ode=D[y[x],{x,4}]-4*D[y[x],{x,3}]==10*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x\int _1^{K[4]}\int _1^{K[3]}e^{4 K[2]} \left (c_1+\int _1^{K[2]}10 e^{-4 K[1]} \sin (2 K[1])dK[1]\right )dK[2]dK[3]dK[4]+x (c_4 x+c_3)+c_2 \end{align*}

✓ Sympy. Time used: 0.059 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*sin(2*x) - 4*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} e^{4 x} + \frac {\sin {\left (2 x \right )}}{8} - \frac {\cos {\left (2 x \right )}}{4} \]