49.23.6 problem 1(f)

Internal problem ID [7764]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page 238
Problem number : 1(f)
Date solved : Sunday, March 30, 2025 at 12:22:58 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }-2 y^{\prime }&=x^{3} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ y = \frac {1}{4} x^{4}+\frac {1}{3} c_1 \,x^{3}+c_2 \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 24

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

\[ y(x)\to \frac {x^4}{4}+\frac {c_1 x^3}{3}+c_2 \]

✓ Sympy. Time used: 0.282 (sec). Leaf size: 14

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

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