84.14.7 problem 7.15

Internal problem ID [22164]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 7. Integrating factors. Supplementary problems
Problem number : 7.15
Date solved : Thursday, October 02, 2025 at 08:33:08 PM
CAS classification : [_separable]

\begin{align*} 1-2 x y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 33

ode=1-2*x*y[x]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.187 (sec). Leaf size: 22

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

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