What is the solution for y^'=y(7-y)-49/4 ,y(0)=a ?

The solution for y^'=y(7-y)-49/4 ,y(0)=a is y=(7at)/(2at-7t+2)-(49t)/(2(2at-7t+2))+(2a)/(2at-7t+2)

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y^'=y(7-y)-49/4 ,y(0)=a

y^{^{'}} = y (7 - y) - \frac{49}{4}, y (0) = a

y = \frac{7 a t}{2 a t - 7 t + 2} - \frac{49 t}{2 ( 2 a t - 7 t + 2 )} + \frac{2 a}{2 a t - 7 t + 2}

Solution steps

y^{'} (t) = y (7 - y) - \frac{49}{4}

Solve separable ODE:

y = \frac{7 a t}{2 a t - 7 t + 2} - \frac{49 t}{2 ( 2 a t - 7 t + 2 )} + \frac{2 a}{2 a t - 7 t + 2}

y = \frac{7 a t}{2 a t - 7 t + 2} - \frac{49 t}{2 ( 2 a t - 7 t + 2 )} + \frac{2 a}{2 a t - 7 t + 2}

y^{^{'}} = \frac{( 3 x ^{4} + y ^{4} )}{x y ^{3}}

\frac{d}{d x} (x^{3} - cos (x))

\int - 7 sin (x) d x

- \frac{7}{x ^{3}}

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

What is the solution for y^'=y(7-y)-49/4 ,y(0)=a ?
The solution for y^'=y(7-y)-49/4 ,y(0)=a is y=(7at)/(2at-7t+2)-(49t)/(2(2at-7t+2))+(2a)/(2at-7t+2)