23.1.557 problem 547

Internal problem ID [5164]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 547
Date solved : Tuesday, September 30, 2025 at 11:47:15 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} 2 x y y^{\prime }&=4 x^{2} \left (1+2 x \right )+y^{2} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

ode:=2*x*y(x)*diff(y(x),x) = 4*x^2*(2*x+1)+y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {\left (4 x^{2}+c_1 +4 x \right ) x} \\ y &= -\sqrt {\left (4 x^{2}+c_1 +4 x \right ) x} \\ \end{align*}

✓ Mathematica. Time used: 0.147 (sec). Leaf size: 52

ode=2*x*y[x]*D[y[x],x]==4*x^2(1+2*x)+y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {x} \sqrt {4 x^2+4 x+c_1}\\ y(x)&\to \sqrt {x} \sqrt {4 x^2+4 x+c_1} \end{align*}

✓ Sympy. Time used: 0.345 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**2*(2*x + 1) + 2*x*y(x)*Derivative(y(x), x) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {x \left (C_{1} + 4 x^{2} + 4 x\right )}, \ y{\left (x \right )} = \sqrt {x \left (C_{1} + 4 x^{2} + 4 x\right )}\right ] \]