What is the solution for 1000-0.017y^'=100y^{''} ?

The solution for 1000-0.017y^'=100y^{''} is y=c_{1}e^{-(17t)/(100000)}+c_{2}+(1000000t)/(17)

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1000-0.017y^'=100y^{''}

1000 - 0.017 y^{^{'}} = 100 y^{^{''}}

y = c_{1} e^{- \frac{17 t}{100000}} + c_{2} + \frac{1000000 t}{17}

Solution steps

1000 - 0.017 y^{'} (t) = 100 y^{''} (t)

Solve linear ODE:

y = c_{1} e^{- \frac{17 t}{100000}} + c_{2} + \frac{1000000 t}{17}

y = c_{1} e^{- \frac{17 t}{100000}} + c_{2} + \frac{1000000 t}{17}

y^{^{''}} + 8 y^{^{'}} + 3 y = 2 x^{2} + 3

y^{^{''}} - 4 y = 2 x^{- 1} e^{3 x}

x^{^{''}} - 3 x^{^{'}} = 8 sin (t)

y^{^{''}} + y = 3 x sin (2 x)

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x^{- 2} e^{x}

What is the solution for 1000-0.017y^'=100y^{''} ?
The solution for 1000-0.017y^'=100y^{''} is y=c_{1}e^{-(17t)/(100000)}+c_{2}+(1000000t)/(17)