What is the solution for y^{''}+y^'=30,y(0)=-94t+60t^2 ?

The solution for y^{''}+y^'=30,y(0)=-94t+60t^2 is y=c_{1}+c_{2}e^{-t}+30t

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y^{''}+y^'=30,y(0)=-94t+60t^2

y^{^{''}} + y^{^{'}} = 30, y (0) = - 94 t + 60 t^{2}

y = c_{1} + c_{2} e^{- t} + 30 t

Solution steps

y^{''} (t) + y^{'} (t) = 30

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + 30 t

y = c_{1} + c_{2} e^{- t} + 30 t

0.5 x^{^{''}} + 5 x^{^{'}} + 12 x = e^{- 4 t} (4 t - 2)

y^{^{''}} - 5 y^{^{'}} + 6 y = x^{3} + 2 x^{2} + 5 x + 2

y^{^{''}} - 5 y^{^{'}} + 4 y = 8 x e^{2} x

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

y^{^{''}} - 12 y^{^{'}} + 37 y = e^{6 x} - x^{2}

What is the solution for y^{''}+y^'=30,y(0)=-94t+60t^2 ?
The solution for y^{''}+y^'=30,y(0)=-94t+60t^2 is y=c_{1}+c_{2}e^{-t}+30t