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Beliebt Rechnen >

D^2(D^2-4D+5)^3y=0

Lösung

D^{2} (D^{2} - 4 D + 5)^{3} y = 0

Lösung

y = c_{1} + c_{2} x + e^{2 x} (c_{3} cos (x) + c_{4} sin (x)) + x e^{2 x} (c_{5} cos (x) + c_{6} sin (x)) + x^{2} e^{2 x} (c_{7} cos (x) + c_{8} sin (x))

Schritte zur Lösung

D^{2} (D^{2} - 4 D + 5)^{3} y = 0

Solve linear ODE:

y = c_{1} + c_{2} x + e^{2 x} (c_{3} cos (x) + c_{4} sin (x)) + x e^{2 x} (c_{5} cos (x) + c_{6} sin (x)) + x^{2} e^{2 x} (c_{7} cos (x) + c_{8} sin (x))

y = c_{1} + c_{2} x + e^{2 x} (c_{3} cos (x) + c_{4} sin (x)) + x e^{2 x} (c_{5} cos (x) + c_{6} sin (x)) + x^{2} e^{2 x} (c_{7} cos (x) + c_{8} sin (x))

Graph

Beliebte Beispiele

20y^{''}+27y^'+9y=0,y(0)=0,y^'(0)=8

20 y^{^{''}} + 27 y^{^{'}} + 9 y = 0, y (0) = 0, y^{^{'}} (0) = 8

3y^{''}+2y^'+y/4 =0

3 y^{^{''}} + 2 y^{^{'}} + \frac{y}{4} = 0

y^{''}+5y^'=0,y^1(0)=1

y^{^{''}} + 5 y^{^{'}} = 0, y^{1} (0) = 1

y^{''}+a^2*n^2*pi^2*y=0

y^{^{''}} + a^{2} \cdot n^{2} \cdot π^{2} \cdot y = 0

3 y^{^{''}} - 4 y^{^{'}} = 0