49.21.8 problem 3(b)

Internal problem ID [7738]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 190
Problem number : 3(b)
Date solved : Monday, January 27, 2025 at 03:11:07 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 5

dsolve([diff(y(x),x)=2*sqrt(y(x)),y(x__0) = 0],y(x), singsol=all)
 

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

DSolve[{D[y[x],x]==2*Sqrt[y[x]],{y[x0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 0 \]