Internal problem ID [5316]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-2 \sqrt {y}=0} \end {gather*} With initial conditions \begin {align*} [y \left (x_{0} \right ) = y_{0}] \end {align*}
✓ Solution by Maple
Time used: 0.421 (sec). Leaf size: 27
dsolve([diff(y(x),x)=2*sqrt(y(x)),y(x__0) = y__0],y(x), singsol=all)
\[ y \relax (x ) = \left (2 x -2 x_{0} \right ) \sqrt {y_{0}}+x^{2}-2 x x_{0} +x_{0}^{2}+y_{0} \]
✓ Solution by Mathematica
Time used: 0.168 (sec). Leaf size: 33
DSolve[{y'[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*}