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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{2} e^{3 t}

Schritte zur Lösung

y^{''} (t) - 2 y^{'} (t) + 5 y = 4 e^{3 t}

Solve linear ODE:

y = e^{t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{2} e^{3 t}

y = e^{t} (c_{1} cos (2 t) + c_{2} sin (2 t)) + \frac{1}{2} e^{3 t}

Graph

Beliebte Beispiele

y^{''}+y=1-\H(t-3pi)

y^{^{''}} + y = 1 - H (t - 3 π)

(d^2y)/(dt^2)+4y=3cos(2t)

\frac{d ^{2} y}{d t ^{2}} + 4 y = 3 cos (2 t)

y^{^{''}} + 2 y = 3 x

y^{''''}-8y^{''}+16y=9e^{2x}

y^{^{''''}} - 8 y^{^{''}} + 16 y = 9 e^{2 x}

y^{''}-4y=(x^2-6)sin(2x)

y^{^{''}} - 4 y = (x^{2} - 6) sin (2 x)