What is the solution for (dy)/(dt)=((4t+y))/(4y-t) ?

The solution for (dy)/(dt)=((4t+y))/(4y-t) is y=(t+sqrt(17t^2+c_{1)})/4 ,y=(t-sqrt(17t^2+c_{1)})/4

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(dy)/(dt)=((4t+y))/(4y-t)

\frac{d y}{d t} = \frac{( 4 t + y )}{4 y - t}

y = \frac{t + 17 t ^{2} + c _{1}}{4}, y = \frac{t - 17 t ^{2} + c _{1}}{4}

Solution steps

\frac{d y}{d t} = \frac{( 4 t + y )}{4 y - t}

Solve exact ODE:

y = \frac{t + 17 t ^{2} + c _{1}}{4}, y = \frac{t - 17 t ^{2} + c _{1}}{4}

y = \frac{t + 17 t ^{2} + c _{1}}{4}, y = \frac{t - 17 t ^{2} + c _{1}}{4}

\frac{d y}{d x} = 1 + x^{2} + y^{2} + x^{2} y^{2}

\frac{d}{d x} (x - 2 x - 2)

\frac{d}{d x} ((1 + x)^{\frac{1}{2}})

\int (cos (x))^{2} \cdot sin (x) d x

\frac{d}{d x} (x^{2} - x - ln (x))

What is the solution for (dy)/(dt)=((4t+y))/(4y-t) ?
The solution for (dy)/(dt)=((4t+y))/(4y-t) is y=(t+sqrt(17t^2+c_{1)})/4 ,y=(t-sqrt(17t^2+c_{1)})/4