73.7.32 problem 32

Internal problem ID [15119]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 32
Date solved : Monday, March 31, 2025 at 01:26:00 PM
CAS classification : [_quadrature]

\begin{align*} \left (x +2\right ) y^{\prime }-x^{3}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=(x+2)*diff(y(x),x)-x^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}}{3}-x^{2}+4 x -8 \ln \left (x +2\right )+c_1 \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 26

ode=(x+2)*D[y[x],x]-x^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \int _1^x\frac {K[1]^3}{K[1]+2}dK[1]+c_1 \]

✓ Sympy. Time used: 0.181 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} + \frac {x^{3}}{3} - x^{2} + 4 x - 8 \log {\left (x + 2 \right )} \]