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

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

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

\frac{d y}{d x} = 3 x (1 + y^{2})

y = tan (\frac{3 x ^{2}}{2} + c_{1})

Solution steps

\frac{d y}{d x} = 3 x (1 + y^{2})

Solve separable ODE:

y = tan (\frac{3 x ^{2}}{2} + c_{1})

y = tan (\frac{3 x ^{2}}{2} + c_{1})

e^{x} sin (y) d x + e^{x} cos (y) d y = 0

\frac{d p}{d t} = 2.5 p - 5 p^{2}

\frac{d y}{d x} = x e^{5 y - 3 x}, y (0) = 1

(x^{2} + 1) \frac{d y}{d x} + 4 x y = x, y (2) = 1

y^{^{'}} = x^{6} y^{- 7}

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