What is the solution for (dy)/(dx)=(4x)/(y-1),y(2)=3 ?

The solution for (dy)/(dx)=(4x)/(y-1),y(2)=3 is y=1+2sqrt(x^2-3)

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(dy)/(dx)=(4x)/(y-1),y(2)=3

\frac{d y}{d x} = \frac{4 x}{y - 1}, y (2) = 3

y = 1 + 2 x^{2} - 3

Solution steps

\frac{d y}{d x} = \frac{4 x}{y - 1}

Solve separable ODE:

y = 1 + 2 x^{2} - 3

y = 1 + 2 x^{2} - 3

4 y^{^{'}} - 4 y - 72 = 3 y^{^{'}}

y^{^{'}} = \frac{( 2 x \cdot y ^{2} + x )}{( x ^{2} \cdot y + y )}

(1 - y^{2})^{0.5} d x = (1 + x^{2}) y d y

\frac{2 d q}{d t} + 6 q = 2

\frac{d y}{d x} y = - 4 x ln (5 x + 2)

What is the solution for (dy)/(dx)=(4x)/(y-1),y(2)=3 ?
The solution for (dy)/(dx)=(4x)/(y-1),y(2)=3 is y=1+2sqrt(x^2-3)