What is the solution for 4(dy)/(dx)=1+2x+3y^2+6xy^2 ?

The solution for 4(dy)/(dx)=1+2x+3y^2+6xy^2 is y=(tan((sqrt(3)(x^2+x+c_{1}))/4))/(sqrt(3))

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4(dy)/(dx)=1+2x+3y^2+6xy^2

4 \frac{d y}{d x} = 1 + 2 x + 3 y^{2} + 6 x y^{2}

y = \frac{tan ( \frac{3 ( x ^{2} + x + c _{1} )}{4} )}{3}

Solution steps

4 \frac{d y}{d x} = 1 + 2 x + 3 y^{2} + 6 x y^{2}

Solve separable ODE:

y = \frac{tan ( \frac{3 ( x ^{2} + x + c _{1} )}{4} )}{3}

y = \frac{tan ( \frac{3 ( x ^{2} + x + c _{1} )}{4} )}{3}

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