6.4.14 problem 16

Internal problem ID [1621]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear Equations. Section 2.3 Page 60
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 04:40:21 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{{2}/{5}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.088 (sec). Leaf size: 18

ode:=diff(y(x),x) = y(x)^(2/5); 
ic:=[y(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (3 x +5\right ) \left (\frac {3 x}{5}+1\right )^{{2}/{3}}}{5} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 23

ode=D[y[x],x]==y[x]^(2/5); 
ic=y[0]==1; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {(3 x+5)^{5/3}}{5\ 5^{2/3}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**(2/5) + Derivative(y(x), x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out