29.7.2 problem 177

Internal problem ID [4777]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 177
Date solved : Tuesday, March 04, 2025 at 07:14:55 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.14 (sec). Leaf size: 23

ode=x D[y[x],x]==y[x](1+2 x y[x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {x}{x^2-c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.179 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - (2*x*y(x) + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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