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Beliebt Rechnen >

(d^4y)/(dx^4)+6(d^2y)/(dx^2)+9y=0

Lösung

\frac{d ^{4} y}{d x ^{4}} + 6 \frac{d ^{2} y}{d x ^{2}} + 9 y = 0

Lösung

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

Schritte zur Lösung

\frac{d ^{4} y}{d x ^{4}} + 6 \frac{d ^{2} y}{d x ^{2}} + 9 y = 0

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

9y^{'''}+12y^{''}+4y^'=0

9 y^{^{'''}} + 12 y^{^{''}} + 4 y^{^{'}} = 0

(D^3-2D^2-5D+6)y=0

(D^{3} - 2 D^{2} - 5 D + 6) y = 0

16y^{''}+88y^'+121y=0

16 y^{^{''}} + 88 y^{^{'}} + 121 y = 0

\frac{y ^{^{''}}}{y} = - 1

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

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