What is the solution for (2y+2)dy-(4x^3+6x)dx=0 ?

The solution for (2y+2)dy-(4x^3+6x)dx=0 is y=-1+sqrt(x^4+3x^2+c_{1)+1},y=-sqrt(x^4+3x^2+c_{1)+1}-1

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(2y+2)dy-(4x^3+6x)dx=0

(2 y + 2) d y - (4 x^{3} + 6 x) d x = 0

y = - 1 + x^{4} + 3 x^{2} + c_{1} + 1, y = - x^{4} + 3 x^{2} + c_{1} + 1 - 1

Solution steps

(2 y + 2) d y - (4 x^{3} + 6 x) d x = 0

Solve separable ODE:

y = - 1 + x^{4} + 3 x^{2} + c_{1} + 1, y = - x^{4} + 3 x^{2} + c_{1} + 1 - 1

y = - 1 + x^{4} + 3 x^{2} + c_{1} + 1, y = - x^{4} + 3 x^{2} + c_{1} + 1 - 1

\frac{d x}{d y} = sin (x) (cos (2 y) - cos^{2} (y))

\frac{d}{d θ} (f (θ)) f (θ) = sin (θ) + csc (θ)

4 ln (x) d x - x sec^{2} (y) d y = 0

6 x^{2} d x - 2 y d y = 0

\frac{d y}{d x} 2 x y = 1

What is the solution for (2y+2)dy-(4x^3+6x)dx=0 ?
The solution for (2y+2)dy-(4x^3+6x)dx=0 is y=-1+sqrt(x^4+3x^2+c_{1)+1},y=-sqrt(x^4+3x^2+c_{1)+1}-1