What is the solution for y^{''}+1000y^'+2470=0 ?

The solution for y^{''}+1000y^'+2470=0 is y=c_{1}+c_{2}e^{-1000t}-(247t)/(100)

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y^{''}+1000y^'+2470=0

y^{^{''}} + 1000 y^{^{'}} + 2470 = 0

y = c_{1} + c_{2} e^{- 1000 t} - \frac{247 t}{100}

Solution steps

y^{''} (t) + 1000 y^{'} (t) + 2470 = 0

Solve linear ODE:

y = c_{1} + c_{2} e^{- 1000 t} - \frac{247 t}{100}

y = c_{1} + c_{2} e^{- 1000 t} - \frac{247 t}{100}

x^{^{''}} + 2 x^{^{'}} + 1 x = e^{- 2 t}, x (0) = 2, x^{^{'}} (0) = 1

y^{^{''}} + 4 y = cos (2 x) + 1

y^{^{''}} + 9 y = sin (3 x), y (0) = 3, y^{^{'}} (0) = - \frac{1}{6}

\frac{d ^{2} y}{d x ^{2}} + y = 4 x cos (x)

y^{^{''}} + 49 y = 3

What is the solution for y^{''}+1000y^'+2470=0 ?
The solution for y^{''}+1000y^'+2470=0 is y=c_{1}+c_{2}e^{-1000t}-(247t)/(100)