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Beliebt Rechnen >

y^{''}-2y^'-7y=1e^{5t}

Lösung

y^{^{''}} - 2 y^{^{'}} - 7 y = 1 e^{5 t}

Lösung

y = c_{1} e^{(1 + 2^{1 + \frac{1}{2}}) t} + c_{2} e^{(1 - 2^{1 + \frac{1}{2}}) t} + \frac{1}{8} e^{5 t}

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) - 7 y = 1 e^{5 t}

Solve linear ODE:

y = c_{1} e^{(1 + 2^{1 + \frac{1}{2}}) t} + c_{2} e^{(1 - 2^{1 + \frac{1}{2}}) t} + \frac{1}{8} e^{5 t}

y = c_{1} e^{(1 + 2^{1 + \frac{1}{2}}) t} + c_{2} e^{(1 - 2^{1 + \frac{1}{2}}) t} + \frac{1}{8} e^{5 t}

Graph

Beliebte Beispiele

9y^{''}+4y^'-y=22

9 y^{^{''}} + 4 y^{^{'}} - y = 22

x^{''}+4x=12*cos(t)

x^{^{''}} + 4 x = 12 \cdot cos (t)

(D^3-2D^2-5D+6)y=e^{4x}

(D^{3} - 2 D^{2} - 5 D + 6) y = e^{4 x}

10y^{''}+20y^'+6260y=100

10 y^{^{''}} + 20 y^{^{'}} + 6260 y = 100

y^{''}+2y^'-8y=24e^{2t}

y^{^{''}} + 2 y^{^{'}} - 8 y = 24 e^{2 t}