7.3.31 problem 31

Internal problem ID [71]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.4 (separable equations). Problems at page 43
Problem number : 31
Date solved : Saturday, March 29, 2025 at 04:28:51 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.118 (sec). Leaf size: 27

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

\[ y = \left (-2 a +2 x \right ) \sqrt {b}+a^{2}-2 x a +x^{2}+b \]

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 33

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

\begin{align*} y(x)\to \left (a+\sqrt {b}-x\right )^2 \\ y(x)\to \left (-a+\sqrt {b}+x\right )^2 \\ \end{align*}

✗ Sympy

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

NotImplementedError : Initial conditions produced too many solutions for constants