12.4.14 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 : Monday, January 27, 2025 at 05:14:16 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*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

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

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

\[ y(x)\to \frac {(3 x+5)^{5/3}}{5\ 5^{2/3}} \]