4.14 problem 16

Internal problem ID [971]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {y^{\prime }-y^{\frac {2}{5}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}

Solution by Maple

Time used: 0.031 (sec). Leaf size: 11

dsolve([diff(y(x),x)=y(x)^(2/5),y(0) = 1],y(x), singsol=all)
 

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

Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 23

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

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