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 : Tuesday, March 04, 2025 at 07:06:22 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(y(x),x)+2*y(x)*(1-x*y(x)^(1/2)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ -\frac {-1+\left ({\mathrm e}^{x} c_{1} +x +1\right ) \sqrt {y \left (x \right )}}{\sqrt {y \left (x \right )}} = 0 \]

✓ Mathematica. Time used: 0.14 (sec). Leaf size: 21

ode=D[y[x],x]+2 y[x] (1-x Sqrt[y[x]])==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.398 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-2*x*sqrt(y(x)) + 2)*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {1}{C_{1}^{2} e^{2 x} + 2 C_{1} x e^{x} + 2 C_{1} e^{x} + x^{2} + 2 x + 1} \]