What is the solution for x^{''}-(pi/2)^2x=0 ?

The solution for x^{''}-(pi/2)^2x=0 is x=c_{1}e^{(pit)/2}+c_{2}e^{-(pit)/2}

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x^{''}-(pi/2)^2x=0

x^{^{''}} - (\frac{π}{2})^{2} x = 0

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

Solution steps

x^{''} (t) - (\frac{π}{2})^{2} x = 0

Solve linear ODE:

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

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

y^{^{''}} - 7 y + 10 y = 0

3 y^{^{''}} + 27 y^{^{'}} + 24 y = 0

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

y^{^{''}} + 13 y^{^{'}} + 18 y = 0, y (0) = 1, y^{^{'}} (0) = 0

81 y^{^{''}} - 54 y^{^{'}} = 0, y (0) = 1, y^{^{'}} (0) = 0

What is the solution for x^{''}-(pi/2)^2x=0 ?
The solution for x^{''}-(pi/2)^2x=0 is x=c_{1}e^{(pit)/2}+c_{2}e^{-(pit)/2}