29.4.13 problem 102

Internal problem ID [4704]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 102
Date solved : Monday, January 27, 2025 at 09:32:31 AM
CAS classification : [_Bernoulli]

\begin{align*} y^{\prime }+2 y \left (1-x \sqrt {y}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (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: 0.140 (sec). Leaf size: 21

DSolve[D[y[x],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*}