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Beliebt Rechnen >

y^{''}-4y^'+3y=4e^{3t},y(0)=2,y^'(0)=7

Lösung

y^{^{''}} - 4 y^{^{'}} + 3 y = 4 e^{3 t}, y (0) = 2, y^{^{'}} (0) = 7

Lösung

y = (2 - \frac{1}{2}) e^{3 t} + \frac{1}{2} e^{t} + 2 t e^{3 t}

Schritte zur Lösung

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

Solve linear ODE:

y = (2 - \frac{1}{2}) e^{3 t} + \frac{1}{2} e^{t} + 2 t e^{3 t}

y = (2 - \frac{1}{2}) e^{3 t} + \frac{1}{2} e^{t} + 2 t e^{3 t}

Graph

Beliebte Beispiele

1/8 y^{''}+4y^'+28x=0,y(0)=0,y^'(0)=3

\frac{1}{8} y^{^{''}} + 4 y^{^{'}} + 28 x = 0, y (0) = 0, y^{^{'}} (0) = 3

-6y^{''}-5y^'-y=-(t^2+2t+2e^{2t})

- 6 y^{^{''}} - 5 y^{^{'}} - y = - (t^{2} + 2 t + 2 e^{2 t})

0.75y^{''}+50y=5t^2

0.75 y^{^{''}} + 50 y = 5 t^{2}

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

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

y^{''}+10y^'+20y=50sinh(5x)

y^{^{''}} + 10 y^{^{'}} + 20 y = 50 sinh (5 x)