What is laplacetransform 2x^2-3x+4 ?

The answer to laplacetransform 2x^2-3x+4 is 4/(s^3)-3/(s^2)+4/s

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laplacetransform 2x^2-3x+4

laplace transform

2 x^{2} - 3 x + 4

\frac{4}{s ^{3}} - \frac{3}{s ^{2}} + \frac{4}{s}

Solution steps

L {2 x^{2} - 3 x + 4}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

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

= 2 L {x^{2}} - 3 L {x} + L {4}

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

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

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

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

Refine

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

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

x \to 18 lim (- 97 x)

y^{^{'}} + y = x y^{3}, y (1) = \frac{1}{2}

\int 12 y^{2} d y

l a pl a ce t r an s f or m 5 t

d er i v a t i v e e^{x^{2}} + x^{3}

What is laplacetransform 2x^2-3x+4 ?
The answer to laplacetransform 2x^2-3x+4 is 4/(s^3)-3/(s^2)+4/s