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Beliebt Rechnen >

x^{''}-2x^'+x=3te^{-t}

Lösung

x^{^{''}} - 2 x^{^{'}} + x = 3 t e^{- t}

Lösung

x = c_{1} e^{t} + c_{2} t e^{t} + \frac{3 e ^{- t} t}{4} + \frac{3}{4} e^{- t}

Schritte zur Lösung

x^{''} (t) - 2 x^{'} (t) + x = 3 t e^{- t}

Solve linear ODE:

x = c_{1} e^{t} + c_{2} t e^{t} + \frac{3 e ^{- t} t}{4} + \frac{3}{4} e^{- t}

x = c_{1} e^{t} + c_{2} t e^{t} + \frac{3 e ^{- t} t}{4} + \frac{3}{4} e^{- t}

Graph

Beliebte Beispiele

y^{''}+(-8)y^'+20y=100x^2-65xe^x

y^{^{''}} + (- 8) y^{^{'}} + 20 y = 100 x^{2} - 65 x e^{x}

y^{''}+4y^'+4y=3x+4

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 x + 4

(D^{2} + D - 12) y = x

y^{''}-8y^'+16y=(x-1)e^{4x}

y^{^{''}} - 8 y^{^{'}} + 16 y = (x - 1) e^{4 x}

y^{''}-5y^'-14y=e^x(x+1)

y^{^{''}} - 5 y^{^{'}} - 14 y = e^{x} (x + 1)