What is the solution for y^{''}-10y+2y=0 ?

The solution for y^{''}-10y+2y=0 is y=c_{1}e^{2^{1+1/2}t}+c_{2}e^{-2^{1+1/2}t}

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y^{''}-10y+2y=0

y^{^{''}} - 10 y + 2 y = 0

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

Solution steps

y^{''} (t) - 10 y + 2 y = 0

Solve linear ODE:

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

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

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What is the solution for y^{''}-10y+2y=0 ?
The solution for y^{''}-10y+2y=0 is y=c_{1}e^{2^{1+1/2}t}+c_{2}e^{-2^{1+1/2}t}