laplacetransform (t+2)^2e^t

Lösung

laplace transformation

(t + 2)^{2} e^{t}

\frac{4 s ^{2} - 4 s + 2}{( s - 1 ) ^{3}}

Schritte zur Lösung

L {e^{t} (t + 2)^{2}}

Wende Transformationsregel an: wenn

L {f (t)} = F (s)

dann

L {e^{a t} f (t)} = F (s - a)

Für

(t + 2)^{2} e^{t} : f (t) = (t + 2)^{2}, a = 1

= L {(t + 2)^{2}} (s - 1)

L {(t + 2)^{2}} : \frac{2}{s ^{3}} + \frac{4}{s ^{2}} + \frac{4}{s}

= \frac{2}{( s - 1 ) ^{3}} + \frac{4}{( s - 1 ) ^{2}} + \frac{4}{( s - 1 )}

= \frac{2}{( s - 1 ) ^{3}} + \frac{4}{( s - 1 ) ^{2}} + \frac{4}{s - 1}

Vereinfache

\frac{2}{( s - 1 ) ^{3}} + \frac{4}{( s - 1 ) ^{2}} + \frac{4}{s - 1} : \frac{4 s ^{2} - 4 s + 2}{( s - 1 ) ^{3}}

= \frac{4 s ^{2} - 4 s + 2}{( s - 1 ) ^{3}}

f (x) = x^{3} e^{x}

\frac{d}{d x} (x^{3} + y^{2})

\frac{\partial}{\partial x} (2 e^{x^{2}})

t an g e n t (\frac{2 x - 1}{x + 1}), 2

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