49.21.7 problem 3(a)

Internal problem ID [7737]
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(a)
Date solved : Monday, January 27, 2025 at 03:11:06 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.104 (sec). Leaf size: 27

dsolve([diff(y(x),x)=2*sqrt(y(x)),y(x__0) = y__0],y(x), singsol=all)
 

\[ y = \left (2 x -2 x_{0} \right ) \sqrt {y_{0}}+x^{2}-2 x x_{0} +x_{0}^{2}+y_{0} \]

✓ Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 33

DSolve[{D[y[x],x]==2*Sqrt[y[x]],{y[x0]==y0}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \left (x-\text {x0}+\sqrt {\text {y0}}\right )^2 \\ y(x)\to \left (-x+\text {x0}+\sqrt {\text {y0}}\right )^2 \\ \end{align*}