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Beliebt Rechnen >

(D^2-2D-3)y=e^{3x}+cos(x)

Lösung

(D^{2} - 2 D - 3) y = e^{3 x} + cos (x)

Lösung

y = c_{1} e^{3 x} + c_{2} e^{- x} + \frac{e ^{3 x} x}{4} - \frac{1}{10} sin (x) - \frac{1}{5} cos (x)

Schritte zur Lösung

(D^{2} - 2 D - 3) y = e^{3 x} + cos (x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- x} + \frac{e ^{3 x} x}{4} - \frac{1}{10} sin (x) - \frac{1}{5} cos (x)

y = c_{1} e^{3 x} + c_{2} e^{- x} + \frac{e ^{3 x} x}{4} - \frac{1}{10} sin (x) - \frac{1}{5} cos (x)

Graph

Beliebte Beispiele

y^{''}+3y^'+7y=cos(t),y(0)=0,y^'(0)=2

y^{^{''}} + 3 y^{^{'}} + 7 y = cos (t), y (0) = 0, y^{^{'}} (0) = 2

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

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

4y^{''}+4y^'+1=0

4 y^{^{''}} + 4 y^{^{'}} + 1 = 0

D (x) = a - 2

(D^3+1)y=3+e^{-x}+5e^{2x}

(D^{3} + 1) y = 3 + e^{- x} + 5 e^{2 x}