What is the solution for (dy)/(dt)=0.07(100-y),y(0)=25 ?

The solution for (dy)/(dt)=0.07(100-y),y(0)=25 is y=-75e^{-(7t)/(100)}+100

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(dy)/(dt)=0.07(100-y),y(0)=25

\frac{d y}{d t} = 0.07 (100 - y), y (0) = 25

y = - 75 e^{- \frac{7 t}{100}} + 100

Solution steps

\frac{d y}{d t} = 0.07 (100 - y)

Solve separable ODE:

y = - 75 e^{- \frac{7 t}{100}} + 100

y = - 75 e^{- \frac{7 t}{100}} + 100

y - 9 \frac{d y}{d t} = 0

\frac{d y}{d x} y = u, u = x^{2} + 2

\frac{d y}{d t} = 3 y, y (6) = 1

y^{^{'}} = - 2 y

- \frac{( - y ^{^{'}} + 72 )}{24} + y + \frac{y ^{^{'}}}{48} = 0

What is the solution for (dy)/(dt)=0.07(100-y),y(0)=25 ?
The solution for (dy)/(dt)=0.07(100-y),y(0)=25 is y=-75e^{-(7t)/(100)}+100