Internal problem ID [2851]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 102.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+2 y \left (1-\sqrt {y}\, x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(diff(y(x),x)+2*y(x)*(1-x*sqrt(y(x))) = 0,y(x), singsol=all)
\[ \frac {1}{\sqrt {y \relax (x )}}-x -1-c_{1} {\mathrm e}^{x} = 0 \]
✓ Solution by Mathematica
Time used: 0.146 (sec). Leaf size: 21
DSolve[y'[x]+2 y[x] (1-x Sqrt[y[x]])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\left (x+c_1 e^x+1\right ){}^2} \\ y(x)\to 0 \\ \end{align*}