56.1.82 problem 81

Internal problem ID [8794]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 81
Date solved : Wednesday, March 05, 2025 at 06:49:25 AM
CAS classification : [_quadrature]

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

With initial conditions

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

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

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

\[ y = 0 \]

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

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

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

✓ Sympy. Time used: 0.170 (sec). Leaf size: 5

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

\[ y{\left (x \right )} = x^{2} \]