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Beliebt Rechnen >

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

Lösung

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

Lösung

y = e^{2 t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{10} e^{- t}

Schritte zur Lösung

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

Solve linear ODE:

y = e^{2 t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{10} e^{- t}

y = e^{2 t} (c_{1} cos (t) + c_{2} sin (t)) + \frac{1}{10} e^{- t}

Graph

Beliebte Beispiele

x^{''}+16x=160sin(4t)

x^{^{''}} + 16 x = 160 sin (4 t)

(d^2y)/(dx^2)-2(dy)/(dx)-3y=2e^{4x}

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} - 3 y = 2 e^{4 x}

y^{''}+4y=t^2+7e^t

y^{^{''}} + 4 y = t^{2} + 7 e^{t}

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

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

d(x)=(100)/(sqrt(pi))e^{-100x^2(x)^2}

d (x) = \frac{100}{π} e^{- 100 x^{2} (x)^{2}}