78.1.12 problem 2.b

Internal problem ID [20938]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 1, First order ODEs. Problems section 1.5
Problem number : 2.b
Date solved : Thursday, October 02, 2025 at 06:49:39 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x +y^{2}-2 x y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 60

ode=(x+y[x]^2)+2*x*y[x]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.268 (sec). Leaf size: 26

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

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