laplacetransform (t^2+1/2)^2

Lösung

laplace transformation

(t^{2} + \frac{1}{2})^{2}

\frac{24}{s ^{5}} + \frac{2}{s ^{3}} + \frac{1}{4 s}

Schritte zur Lösung

L {(t^{2} + \frac{1}{2})^{2}}

Schreibe

(t^{2} + \frac{1}{2})^{2}

um:

t^{4} + t^{2} + \frac{1}{4}

= L {t^{4} + t^{2} + \frac{1}{4}}

Verwende die lineare Eigenschaft der Laplace-Transformation:

Für Funktionen

f (t), g (t)

und Konstanten

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {t^{4}} + L {t^{2}} + L {\frac{1}{4}}

L {t^{4}} : \frac{24}{s ^{5}}

L {t^{2}} : \frac{2}{s ^{3}}

L {\frac{1}{4}} : \frac{1}{4 s}

= \frac{24}{s ^{5}} + \frac{2}{s ^{3}} + \frac{1}{4 s}

(x^{2} + 2 y^{2}) d x - x y d y = 0

t an g e n t y = 2 sin (x), at x = \frac{3}{4} π

d er i v a t i v e h (x) = \frac{3 x ^{3} - 3}{ln ( x )}

a re a y = \frac{3}{x}, y = 9 x, y = \frac{1}{9 x}

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) d x