36.1.33 problem 30

Internal problem ID [6288]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page 46
Problem number : 30
Date solved : Sunday, March 30, 2025 at 10:49:16 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\left (x -3\right ) \left (y+1\right )^{{2}/{3}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=diff(y(x),x) = (x-3)*(1+y(x))^(2/3); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {x^{2}}{2}-3 x -3 \left (y+1\right )^{{1}/{3}}+c_1 = 0 \]

✓ Mathematica. Time used: 0.206 (sec). Leaf size: 67

ode=D[y[x],x]==(x-3)*(y[x]+1)^(2/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{216} \left (x^6-18 x^5+6 (18+c_1) x^4-72 (3+c_1) x^3+12 c_1 (18+c_1) x^2-72 c_1{}^2 x+8 \left (-27+c_1{}^3\right )\right ) \\ y(x)\to -1 \\ \end{align*}

✓ Sympy. Time used: 0.323 (sec). Leaf size: 61

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3 - x)*(y(x) + 1)**(2/3) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}^{3}}{27} + \frac {C_{1}^{2} x^{2}}{18} - \frac {C_{1}^{2} x}{3} + \frac {C_{1} x^{4}}{36} - \frac {C_{1} x^{3}}{3} + C_{1} x^{2} + \frac {x^{6}}{216} - \frac {x^{5}}{12} + \frac {x^{4}}{2} - x^{3} - 1 \]