What is the solution for y^{'''}=e^{-0.2x} ?

The solution for y^{'''}=e^{-0.2x} is y=-125e^{-0.2x}+0.5c_{1}x^2+c_{2}x+c_{3}

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y^{'''}=e^{-0.2x}

y^{^{'''}} = e^{- 0.2 x}

y = - 125 e^{- 0.2 x} + 0.5 c_{1} x^{2} + c_{2} x + c_{3}

Solution steps

y^{'''} (x) = e^{- 0.2 x}

Solve

y^{'''} (x) = e^{- 0.2 x} : y^{''} (x) = - 5 e^{- 0.2 x} + c_{1}

Solve

y^{''} (x) = - 5 e^{- 0.2 x} + c_{1} : y^{'} (x) = 25 e^{- 0.2 x} + c_{1} x + c_{2}

Solve

y^{'} (x) = 25 e^{- 0.2 x} + c_{1} x + c_{2} : y = - 125 e^{- 0.2 x} + 0.5 c_{1} x^{2} + c_{2} x + c_{3}

y = - 125 e^{- 0.2 x} + 0.5 c_{1} x^{2} + c_{2} x + c_{3}

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What is the solution for y^{'''}=e^{-0.2x} ?
The solution for y^{'''}=e^{-0.2x} is y=-125e^{-0.2x}+0.5c_{1}x^2+c_{2}x+c_{3}