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Popular >

y^'=r-ky

Solution

y^{^{'}} = r - k y

Solution

y = - \frac{e ^{- k t - c_{1}}}{k} + \frac{r}{k}

Solution steps

y^{'} (t) = r - k y (t)

Solve separable ODE:

y = - \frac{e ^{- k t - c_{1}}}{k} + \frac{r}{k}

y = - \frac{e ^{- k t - c_{1}}}{k} + \frac{r}{k}

Popular Examples

limit as x approaches-1 of x|x+1|

x \to - 1 lim (x ∣ x + 1 ∣)

derivative of f(x)=7y^7-4y^6+35y^4-24y^2 derivative of

f (x) = 7 y^{7} - 4 y^{6} + 35 y^{4} - 24 y^{2}

limit as x approaches 0 of (((x^2+3)))/x

x \to 0 lim (\frac{( ( x ^{2} + 3 ) )}{x})

tangent of f(x)=(8-9x)(8+9x),\at x=9 tangent of

f (x) = (8 - 9 x) (8 + 9 x), at x = 9

limit as x approaches infinity of x^2+2

x \to \infty lim (x^{2} + 2)

Frequently Asked Questions (FAQ)

What is the solution for y^'=r-ky ?
The solution for y^'=r-ky is y=-(e^{-kt-c_{1}})/k+r/k