89.7.29 problem 28

Internal problem ID [24460]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 61
Problem number : 28
Date solved : Thursday, October 02, 2025 at 10:38:54 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2}+6 y^{2}-4 x y y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 14

ode:=x^2+6*y(x)^2-4*x*y(x)*diff(y(x),x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\sqrt {6 x -2}\, x}{2} \]

✓ Mathematica. Time used: 0.198 (sec). Leaf size: 21

ode=( x^2+6*y[x]^2)-(4*x*y[x])*D[y[x],x]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x \sqrt {3 x-1}}{\sqrt {2}} \end{align*}

✓ Sympy. Time used: 0.279 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 - 4*x*y(x)*Derivative(y(x), x) + 6*y(x)**2,0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x \sqrt {6 x - 2}}{2} \]