What is the solution for y^{''}-0.1y=0 ?

The solution for y^{''}-0.1y=0 is y=c_{1}e^{t/(sqrt(10))}+c_{2}e^{-t/(sqrt(10))}

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y^{''}-0.1y=0

y^{^{''}} - 0.1 y = 0

y = c_{1} e^{\frac{t}{10}} + c_{2} e^{- \frac{t}{10}}

Solution steps

y^{''} (t) - 0.1 y = 0

Solve linear ODE:

y = c_{1} e^{\frac{t}{10}} + c_{2} e^{- \frac{t}{10}}

y = c_{1} e^{\frac{t}{10}} + c_{2} e^{- \frac{t}{10}}

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

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

y^{^{'''}} + 9 y^{^{'}} = 0, y^{^{'}} (0) = - 21

16 y^{^{''}} + 8 y^{^{'}} + 145 y = 0

2 \frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 51 y = 0

What is the solution for y^{''}-0.1y=0 ?
The solution for y^{''}-0.1y=0 is y=c_{1}e^{t/(sqrt(10))}+c_{2}e^{-t/(sqrt(10))}