34.3.18 problem 25 (c)

Internal problem ID [7909]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 25 (c)
Date solved : Tuesday, September 30, 2025 at 05:09:57 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 30

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

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

✓ Mathematica. Time used: 0.134 (sec). Leaf size: 44

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 -\sqrt {x} \sqrt {-\log (x)+c_1}\\ y(x)&\to \sqrt {x} \sqrt {-\log (x)+c_1} \end{align*}

✓ Sympy. Time used: 0.285 (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)
 

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