81.6.27 problem 7-26

Internal problem ID [21573]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 7. Linear Differential Equations. Page 101.
Problem number : 7-26
Date solved : Thursday, October 02, 2025 at 07:50:01 PM
CAS classification : [_rational, _Bernoulli]

\begin{align*} y \left (6 y^{2}-x -1\right )+2 x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 54

ode:=y(x)*(6*y(x)^2-x-1)+2*x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\sqrt {\left (c_1 \,{\mathrm e}^{-x}+6\right ) x}}{c_1 \,{\mathrm e}^{-x}+6} \\ y &= -\frac {\sqrt {\left (c_1 \,{\mathrm e}^{-x}+6\right ) x}}{c_1 \,{\mathrm e}^{-x}+6} \\ \end{align*}

✓ Mathematica. Time used: 0.516 (sec). Leaf size: 65

ode=y[x]*(6*y[x]^2-x-1)+2*x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {e^{x/2} \sqrt {x}}{\sqrt {6 e^x+c_1}}\\ y(x)&\to \frac {e^{x/2} \sqrt {x}}{\sqrt {6 e^x+c_1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.501 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), x) + (-x + 6*y(x)**2 - 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {\frac {x e^{x}}{C_{1} + 6 e^{x}}}, \ y{\left (x \right )} = \sqrt {\frac {x e^{x}}{C_{1} + 6 e^{x}}}\right ] \]