81.11.29 problem 15-28

Internal problem ID [21653]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 15. Method of undetermined coefficients. Page 337.
Problem number : 15-28
Date solved : Thursday, October 02, 2025 at 07:59:28 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-y^{\prime \prime }&=3 x^{2}+4 \sin \left (x \right )-2 \cos \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-diff(diff(y(x),x),x) = 3*x^2+4*sin(x)-2*cos(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.236 (sec). Leaf size: 46

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

\begin{align*} y(x)&\to -\frac {x^4}{4}-3 x^2+2 \sin (x)-\cos (x)+c_4 x+c_1 e^x+c_2 e^{-x}+c_3 \end{align*}

✓ Sympy. Time used: 0.077 (sec). Leaf size: 36

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

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