What is the solution for y(x^3dy+y^3dx)=0 ?

The solution for y(x^3dy+y^3dx)=0 is y=sqrt(-(x^2)/(1+2c_{1)x^2)},y=-sqrt(-(x^2)/(1+2c_{1)x^2)}

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y(x^3dy+y^3dx)=0

y (x^{3} d y + y^{3} d x) = 0

y = - \frac{x ^{2}}{1 + 2 c _{1} x ^{2}}, y = - - \frac{x ^{2}}{1 + 2 c _{1} x ^{2}}

Solution steps

y (x^{3} d y + y^{3} d x) = 0

Solve separable ODE:

y = - \frac{x ^{2}}{1 + 2 c _{1} x ^{2}}, y = - - \frac{x ^{2}}{1 + 2 c _{1} x ^{2}}

y = - \frac{x ^{2}}{1 + 2 c _{1} x ^{2}}, y = - - \frac{x ^{2}}{1 + 2 c _{1} x ^{2}}

\frac{d V}{d t} = 4 kπ (\frac{3 V}{4 π})^{\frac{2}{3}}

\frac{d t}{d x} = \frac{( 3000 - x )}{100}

3 x^{^{'}} + 21 x = 0

y^{^{'}} = (2 sin (2 x) cos (2 x)) y^{2}, y (0) = 2

\frac{d y}{d t} y = cos (9 t - 13)

What is the solution for y(x^3dy+y^3dx)=0 ?
The solution for y(x^3dy+y^3dx)=0 is y=sqrt(-(x^2)/(1+2c_{1)x^2)},y=-sqrt(-(x^2)/(1+2c_{1)x^2)}