87.16.11 problem 11

Internal problem ID [23580]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 119
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:43:09 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 35

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

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

✓ Sympy. Time used: 0.058 (sec). Leaf size: 26

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

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