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Popular Calculus >

(D^4-2D^2+4)y=0

Solution

(D^{4} - 2 D^{2} + 4) y = 0

Solution

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

Solution steps

(D^{4} - 2 D^{2} + 4) y = 0

Solve linear ODE:

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

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

Graph

Popular Examples

4y^{''}-8y^'+3y=0,y(0)=2,y^'(0)=1

(D^3-2D^2-D+2)y=0

y^{''}+5y^'-y=0

y^{'''}+9y^{''}+20y^'=0

y^{''}+8y^'+4y=0,y(0)=0,y^'(0)=1

Frequently Asked Questions (FAQ)

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