What is the solution for (dy)/(dx)=4-y^2 ?

The solution for (dy)/(dx)=4-y^2 is y=-(2e^{4x+4c_{1}})/(1-e^{4(x+c_{1))}}-2/(1-e^{4(x+c_{1))}}

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(dy)/(dx)=4-y^2

\frac{d y}{d x} = 4 - y^{2}

y = - \frac{2 e ^{4 x + 4 c_{1}}}{1 - e ^{4 (x + c_{1})}} - \frac{2}{1 - e ^{4 (x + c_{1})}}

Solution steps

\frac{d y}{d x} = 4 - y^{2}

Solve separable ODE:

y = - \frac{2 e ^{4 x + 4 c_{1}}}{1 - e ^{4 (x + c_{1})}} - \frac{2}{1 - e ^{4 (x + c_{1})}}

y = - \frac{2 e ^{4 x + 4 c_{1}}}{1 - e ^{4 (x + c_{1})}} - \frac{2}{1 - e ^{4 (x + c_{1})}}

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

x + y y^{^{'}} = 0, y (0) = 9

(2 x - 1) d x + (3 y + 7) d y = 0, y (- 1) = 2

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

\frac{d y}{d x} = x^{3} y^{2}

What is the solution for (dy)/(dx)=4-y^2 ?
The solution for (dy)/(dx)=4-y^2 is y=-(2e^{4x+4c_{1}})/(1-e^{4(x+c_{1))}}-2/(1-e^{4(x+c_{1))}}