30.8.1 problem 7

Internal problem ID [7578]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Review problem. (G) Multiple Solutions. page 86
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 04:54:26 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (2\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 5

ode:=diff(y(x),x) = 2*y(x)^(2/3); 
ic:=[y(2) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 6

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

\begin{align*} y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.113 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = \frac {8 x^{3}}{27} - \frac {16 x^{2}}{9} + \frac {32 x}{9} - \frac {64}{27} \]