What is the solution for (x^2-3)(dy)/(dx)=x(y^2+16),y(2)=4 ?

The solution for (x^2-3)(dy)/(dx)=x(y^2+16),y(2)=4 is y=4tan(2ln(x^2-3)+pi/4)

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(x^2-3)(dy)/(dx)=x(y^2+16),y(2)=4

(x^{2} - 3) \frac{d y}{d x} = x (y^{2} + 16), y (2) = 4

y = 4 tan (2 ln (x^{2} - 3) + \frac{π}{4})

Solution steps

(x^{2} - 3) \frac{d y}{d x} = x (y^{2} + 16)

Solve separable ODE:

y = 4 tan (2 ln (x^{2} - 3) + \frac{π}{4})

y = 4 tan (2 ln (x^{2} - 3) + \frac{π}{4})

\frac{d y}{d x} = \frac{x + 2}{y ^{2}}

y^{^{'}} = \frac{4 x}{1 + 2 y}, y (9) = 0

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

x y^{^{'}} - (x + 1) y = 0

x y^{2} cos (x) d x - 3 x^{2} y cos (x) d y = 0, y (1) = 1

What is the solution for (x^2-3)(dy)/(dx)=x(y^2+16),y(2)=4 ?
The solution for (x^2-3)(dy)/(dx)=x(y^2+16),y(2)=4 is y=4tan(2ln(x^2-3)+pi/4)