15.12.14 problem 14

Internal problem ID [3158]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 14
Date solved : Sunday, March 30, 2025 at 01:19:56 AM
CAS classification : [[_high_order, _missing_y]]

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

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

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

\[ y = \left (c_1 x -2 c_1 +c_2 \right ) {\mathrm e}^{x}+\frac {x^{4}}{12}+\frac {2 x^{3}}{3}+3 x^{2}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.107 (sec). Leaf size: 46

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

\[ y(x)\to \frac {x^4}{12}+\frac {2 x^3}{3}+3 x^2+c_4 x+c_1 e^x+c_2 e^x (x-2)+c_3 \]

✓ Sympy. Time used: 0.120 (sec). Leaf size: 34

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

\[ y{\left (x \right )} = C_{1} + C_{4} e^{x} + \frac {x^{4}}{12} + \frac {2 x^{3}}{3} + 3 x^{2} + x \left (C_{2} + C_{3} e^{x}\right ) \]