15.11.14 problem 14

Internal problem ID [3124]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 14
Date solved : Tuesday, March 04, 2025 at 04:00:42 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }&=x^{2}+8 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x) = x^2+8; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {65 x^{2}}{64}-\frac {x^{3}}{48}-\frac {x^{4}}{48}+\frac {{\mathrm e}^{4 x} c_{1}}{16}+c_2 x +c_3 \]

✓ Mathematica. Time used: 0.174 (sec). Leaf size: 41

ode=D[y[x],{x,3}]-4*D[y[x],{x,2}]==x^2+8; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{192} \left (-4 x^4-4 x^3-195 x^2+12 c_1 e^{4 x}\right )+c_3 x+c_2 \]

✓ Sympy. Time used: 0.092 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} e^{4 x} - \frac {x^{4}}{48} - \frac {x^{3}}{48} - \frac {65 x^{2}}{64} \]