What is the solution for (d^4y)/(dx^4)-(d^2y)/(dx^2)+4y=0 ?

The solution for (d^4y)/(dx^4)-(d^2y)/(dx^2)+4y=0 is

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(d^4y)/(dx^4)-(d^2y)/(dx^2)+4y=0

\frac{d ^{4} y}{d x ^{4}} - \frac{d ^{2} y}{d x ^{2}} + 4 y = 0

y = e^{\frac{5 x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + e^{- \frac{5 x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2}))

Solution steps

\frac{d ^{4} y}{d x ^{4}} - \frac{d ^{2} y}{d x ^{2}} + 4 y = 0

Solve linear ODE:

y = e^{\frac{5 x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + e^{- \frac{5 x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2}))

y = e^{\frac{5 x}{2}} (c_{1} cos (\frac{3 x}{2}) + c_{2} sin (\frac{3 x}{2})) + e^{- \frac{5 x}{2}} (c_{3} cos (\frac{3 x}{2}) + c_{4} sin (\frac{3 x}{2}))

\frac{d ^{2} y}{d x ^{2}} = 0.15 y, y (0) = 240, y (10) = 150

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 2, y^{^{'}} (0) = - 16

y = 10 y^{^{''}}

y^{^{''}} - 2 y^{^{'}} - 6 y = 0

y^{^{''}} + 3 y^{^{'}} - 18 y = 0, y (0) = - 1, y^{^{'}} (0) = 24

What is the solution for (d^4y)/(dx^4)-(d^2y)/(dx^2)+4y=0 ?
The solution for (d^4y)/(dx^4)-(d^2y)/(dx^2)+4y=0 is