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Beliebt Rechnen >

laplacetransform ((2te^{-3t}))/5+3t*sin(t)

Lösung

laplace transformation

\frac{( 2 t e ^{- 3 t} )}{5} + 3 t \cdot sin (t)

Lösung

\frac{2}{5 ( s + 3 ) ^{2}} + \frac{6 s}{( s ^{2} + 1 ) ^{2}}

Schritte zur Lösung

L {\frac{( 2 e ^{- 3 t} t )}{5} + 3 t sin (t)}

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 {\frac{2 t e ^{- 3 t}}{5}} + 3 L {t sin (t)}

L {\frac{2 t e ^{- 3 t}}{5}} : \frac{2}{5 ( s + 3 ) ^{2}}

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

= \frac{2}{5 ( s + 3 ) ^{2}} + 3 \cdot \frac{2 s}{( s ^{2} + 1 ) ^{2}}

Fasse

\frac{2}{5 ( s + 3 ) ^{2}} + 3 \frac{2 s}{( s ^{2} + 1 ) ^{2}}

zusammen:

\frac{2}{5 ( s + 3 ) ^{2}} + \frac{6 s}{( s ^{2} + 1 ) ^{2}}

= \frac{2}{5 ( s + 3 ) ^{2}} + \frac{6 s}{( s ^{2} + 1 ) ^{2}}

Beliebte Beispiele

(13+x^2)y^'-2xy=0

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

(\partial)/(\partial x)(yx+2x+{g}(y))

\frac{\partial}{\partial x} (y x + 2 x + g (y))

y^{^{'}} = - x y

tangent f(x)=x^3-2x+2,\at x=3

t an g e n t f (x) = x^{3} - 2 x + 2, at x = 3

(\partial)/(\partial x)(ln(ax+by)+c^{x+y})

\frac{\partial}{\partial x} (ln (a x + b y) + c^{x + y})