56.1.82 problem 81

Internal problem ID [8794]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 81
Date solved : Monday, January 27, 2025 at 05:00:49 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

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

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

\[ y = 0 \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 8

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

\[ y(x)\to x^2 \]