What is the solution for (dy)/(dt)= t/(y-2),y(-1)=0 ?

The solution for (dy)/(dt)= t/(y-2),y(-1)=0 is y=2-sqrt(t^2+3)

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(dy)/(dt)= t/(y-2),y(-1)=0

\frac{d y}{d t} = \frac{t}{y - 2}, y (- 1) = 0

y = 2 - t^{2} + 3

Solution steps

\frac{d y}{d t} = \frac{t}{y - 2}

Solve separable ODE:

y = 2 - t^{2} + 3

y = 2 - t^{2} + 3

\frac{d}{d x} (\frac{3}{5 x ^{2}})

\int sin (x) sin (2 x) cos (3 x) d x

\frac{\partial}{\partial x} (\frac{- x y}{x ^{2} + y ^{2}})

x \to 3 + lim (\frac{3 - x}{x ^{2} - 9})

What is the solution for (dy)/(dt)= t/(y-2),y(-1)=0 ?
The solution for (dy)/(dt)= t/(y-2),y(-1)=0 is y=2-sqrt(t^2+3)