What is the solution for y^{''}-k*y=0 ?

The solution for y^{''}-k*y=0 is y=c_{1}e^{sqrt(k)t}+c_{2}e^{-sqrt(k)t}

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y^{''}-k*y=0

y^{^{''}} - k \cdot y = 0

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

Solution steps

y^{''} (t) - k \cdot y = 0

Solve linear ODE:

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

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

(6 d^{3} + 5 d^{2}) y = 0

y^{^{'''}} + 7 y^{^{''}} + 14 y^{^{'}} + 8 y = 0

\frac{d ^{4} y}{d t ^{4}} + 2 y^{^{''}} + y = 0

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = - 5

y^{^{''}} + y^{^{'}} = 0, y (0) = 2

What is the solution for y^{''}-k*y=0 ?
The solution for y^{''}-k*y=0 is y=c_{1}e^{sqrt(k)t}+c_{2}e^{-sqrt(k)t}