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Beliebt Rechnen >

16(d^4y)/(dx^4)+16(d^2y)/(dx^2)+4y=0

Lösung

16 \frac{d ^{4} y}{d x ^{4}} + 16 \frac{d ^{2} y}{d x ^{2}} + 4 y = 0

Lösung

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

Schritte zur Lösung

16 \frac{d ^{4} y}{d x ^{4}} + 16 \frac{d ^{2} y}{d x ^{2}} + 4 y = 0

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{^{''}} + y^{^{'}} = 6 y

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

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

y^{'''}-2y^{''}-9y^'+18y=0

y^{^{'''}} - 2 y^{^{''}} - 9 y^{^{'}} + 18 y = 0

4y^{''}-4y^'-3y=0,y(0)=5

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0, y (0) = 5

y^{''}+2y^'-8y=0,y(0)=8,y^'(0)=-14

y^{^{''}} + 2 y^{^{'}} - 8 y = 0, y (0) = 8, y^{^{'}} (0) = - 14