laplacetransform f(t)=cos(2t)

解答

拉普拉斯变换

f (t) = cos (2 t)

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

求解步骤

L {cos (2 t)}

使用拉普拉斯变换表:

L {cos (a t)} = \frac{s}{s ^{2} + a ^{2}}

L {cos (2 t)} = \frac{s}{s ^{2} + 2 ^{2}}

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

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

x y \frac{d y}{d x} = 1

\int + \frac{x}{x ^{2} + 1} d x

l a pl a ce t r an s f or m t^{3} sin (2 t)

x \cdot \frac{d y}{d x} - y = x^{2} sin (x)

\int y - 1 d y