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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- t} + c_{2} e^{\frac{t}{3}} + t^{2} + 5 t + 16 + \frac{2}{15} e^{2 t}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{\frac{t}{3}} + t^{2} + 5 t + 16 + \frac{2}{15} e^{2 t}

y = c_{1} e^{- t} + c_{2} e^{\frac{t}{3}} + t^{2} + 5 t + 16 + \frac{2}{15} e^{2 t}

Graph

Beliebte Beispiele

x^{'''}-4x^{''}+5x^'-2x=2t+3

x^{^{'''}} - 4 x^{^{''}} + 5 x^{^{'}} - 2 x = 2 t + 3

y^{''}+4y=sin(2x+3)

y^{^{''}} + 4 y = sin (2 x + 3)

(d^2+2d+2)y=3e^xsin(x)

(d^{2} + 2 d + 2) y = 3 e^{x} sin (x)

y^{''}-5y^'+6y=x-e^x

y^{^{''}} - 5 y^{^{'}} + 6 y = x - e^{x}

y^{''}+4y^'+40y=4e^{-2t}cos(6t)

y^{^{''}} + 4 y^{^{'}} + 40 y = 4 e^{- 2 t} cos (6 t)