Internal problem ID [3360]
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]
\[ \boxed {y^{\prime }+2 y \left (1-\sqrt {y}\, x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x)+2*y(x)*(1-x*sqrt(y(x))) = 0,y(x), singsol=all)
\[ -\frac {-1+\left ({\mathrm e}^{x} c_{1} +x +1\right ) \sqrt {y \left (x \right )}}{\sqrt {y \left (x \right )}} = 0 \]
✓ Solution by Mathematica
Time used: 0.147 (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*}