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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} - e^{- 2 t} ln (t) - e^{- 2 t}

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} - e^{- 2 t} ln (t) - e^{- 2 t}

y = c_{1} e^{- 2 t} + c_{2} t e^{- 2 t} - e^{- 2 t} ln (t) - e^{- 2 t}

Graph

Beliebte Beispiele

derivative of tan(sqrt(x^2-1))

\frac{d}{d x} (tan (x^{2} - 1))

y^{''}-y^'-20y=0

y^{^{''}} - y^{^{'}} - 20 y = 0

(d^2)/(dx^2)(3x-4x^{9/10})

\frac{d ^{2}}{d x ^{2}} (3 x - 4 x^{\frac{9}{10}})

implicit (dy)/(dx),e^y=x+y

im pl i c i t \frac{d y}{d x}, e^{y} = x + y

sum from n=2 to infinity of (-0.75)^n

n = 2 \sum \infty (- 0.75)^{n}