What is the solution for y^{'''}+2y^{''}+y^'=10 ?

The solution for y^{'''}+2y^{''}+y^'=10 is y=c_{1}+c_{2}e^{-t}+c_{3}te^{-t}+10t

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y^{'''}+2y^{''}+y^'=10

y^{^{'''}} + 2 y^{^{''}} + y^{^{'}} = 10

y = c_{1} + c_{2} e^{- t} + c_{3} t e^{- t} + 10 t

Solution steps

y^{'''} (t) + 2 y^{''} (t) + y^{'} (t) = 10

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + c_{3} t e^{- t} + 10 t

y = c_{1} + c_{2} e^{- t} + c_{3} t e^{- t} + 10 t

What is the solution for y^{'''}+2y^{''}+y^'=10 ?
The solution for y^{'''}+2y^{''}+y^'=10 is y=c_{1}+c_{2}e^{-t}+c_{3}te^{-t}+10t