What is the solution for y^{''}+cy-c-k=0 ?

The solution for y^{''}+cy-c-k=0 is y=c_{1}cos(sqrt(c)t)+c_{2}sin(sqrt(c)t)+(c+k)/c

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y^{''}+cy-c-k=0

y^{^{''}} + cy - c - k = 0

y = c_{1} cos (c t) + c_{2} sin (c t) + \frac{c + k}{c}

Solution steps

y^{''} (t) + cy (t) - c - k = 0

Solve linear ODE:

y = c_{1} cos (c t) + c_{2} sin (c t) + \frac{c + k}{c}

y = c_{1} cos (c t) + c_{2} sin (c t) + \frac{c + k}{c}

y^{^{''}} + 4 y^{^{'}} + 4 y = e^{3 x}

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

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 159 = 0

y^{^{''}} + 3 y^{^{'}} + 3 y = 6 sin (2 t)

y^{^{''}} - 14 y^{^{'}} + 49 y = 14 x + 3

What is the solution for y^{''}+cy-c-k=0 ?
The solution for y^{''}+cy-c-k=0 is y=c_{1}cos(sqrt(c)t)+c_{2}sin(sqrt(c)t)+(c+k)/c