What is the solution for y^'+ky=e^{-7kx} ?

The solution for y^'+ky=e^{-7kx} is y=-1/(6ke^{7kx)}+(c_{1})/(e^{kx)}

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y^'+ky=e^{-7kx}

y^{^{'}} + k y = e^{- 7 k x}

y = - \frac{1}{6 k e ^{7 k x}} + \frac{c _{1}}{e ^{k x}}

Solution steps

y^{'} (x) + k y (x) = e^{- 7 k x}

Solve linear ODE:

y = - \frac{1}{6 k e ^{7 k x}} + \frac{c _{1}}{e ^{k x}}

y = - \frac{1}{6 k e ^{7 k x}} + \frac{c _{1}}{e ^{k x}}

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f (x) = 2 x^{3} - x^{2} + 3 x, at x = 1

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What is the solution for y^'+ky=e^{-7kx} ?
The solution for y^'+ky=e^{-7kx} is y=-1/(6ke^{7kx)}+(c_{1})/(e^{kx)}