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Beliebt Rechnen >

3y^{''}-6y^'+30y=15sin(x)

Lösung

3 y^{^{''}} - 6 y^{^{'}} + 30 y = 15 sin (x)

Lösung

y = e^{x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{9}{17} sin (x) + \frac{2}{17} cos (x)

Schritte zur Lösung

3 y^{''} (x) - 6 y^{'} (x) + 30 y = 15 sin (x)

Solve linear ODE:

y = e^{x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{9}{17} sin (x) + \frac{2}{17} cos (x)

y = e^{x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{9}{17} sin (x) + \frac{2}{17} cos (x)

Graph

Beliebte Beispiele

y^{''}-2y^'+26y=e^xcos(5x)

y^{^{''}} - 2 y^{^{'}} + 26 y = e^{x} cos (5 x)

y^{''}-4y^'+4y=2xe^{2x}

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 x e^{2 x}

x^{''}+5x^'+6x=12e^{-5t}+12e^{-t}+24

x^{^{''}} + 5 x^{^{'}} + 6 x = 12 e^{- 5 t} + 12 e^{- t} + 24

y^{''}+6y^'+5y=20

y^{^{''}} + 6 y^{^{'}} + 5 y = 20

y^{''}+y=e^{3t}-4tcos(5t)

y^{^{''}} + y = e^{3 t} - 4 t cos (5 t)