What is laplacetransform t/2 ?

The answer to laplacetransform t/2 is 1/(2s^2)

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laplacetransform t/2

laplace transform

\frac{t}{2}

\frac{1}{2 s ^{2}}

Solution steps

L {\frac{t}{2}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= \frac{1}{2} L {t}

L {t} : \frac{1}{s ^{2}}

= \frac{1}{2} \cdot \frac{1}{s ^{2}}

Refine

\frac{1}{2} \frac{1}{s ^{2}} : \frac{1}{2 s ^{2}}

= \frac{1}{2 s ^{2}}

y = x, x = 9, y = 0

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

3 y^{^{''}} + 5 y^{^{'}} + 2 y = 0

\int (3 + 2 cos (x))^{2} d x

x \to 2 lim (\frac{6 x}{x - 2})