What is the solution for (dy)/(dx)=sqrt(y^2-25) ?

The solution for (dy)/(dx)=sqrt(y^2-25) is y= 5/(2e^{x+c_{1)}}+(5e^{x+c_{1}})/2

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(dy)/(dx)=sqrt(y^2-25)

\frac{d y}{d x} = y^{2} - 25

y = \frac{5}{2 e ^{x + c_{1}}} + \frac{5 e ^{x + c_{1}}}{2}

Solution steps

\frac{d y}{d x} = y^{2} - 25

Solve separable ODE:

y = \frac{5}{2 e ^{x + c_{1}}} + \frac{5 e ^{x + c_{1}}}{2}

y = \frac{5}{2 e ^{x + c_{1}}} + \frac{5 e ^{x + c_{1}}}{2}

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

\frac{d y}{d x} = 14 x sec (y)

y^{^{'}} = - \frac{x - 3}{36 y - 108}, y (3) = 4

\frac{d S}{d t} = 0.04 - \frac{S}{( 1140 )}

5 y^{^{'}} = 4 x + 2 x y

What is the solution for (dy)/(dx)=sqrt(y^2-25) ?
The solution for (dy)/(dx)=sqrt(y^2-25) is y= 5/(2e^{x+c_{1)}}+(5e^{x+c_{1}})/2