laplacetransform te^{7t}

解答

拉普拉斯变换

t e^{7 t}

\frac{1}{( s - 7 ) ^{2}}

求解步骤

L {e^{7 t} t}

使用拉普拉斯变换表:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

对于

t e^{7 t} : f (t) = e^{7 t}, k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{7 t}})

L {e^{7 t}} : \frac{1}{s - 7}

\frac{d}{d s} (\frac{1}{s - 7}) = - \frac{1}{( s - 7 ) ^{2}}

= (- 1)^{1} (- \frac{1}{( s - 7 ) ^{2}})

= \frac{1}{( s - 7 ) ^{2}}

\frac{d y}{d t} = 3 y + y^{5}, y (0) = 1

\int x sec (3 x^{2} + 1) d x

6 \frac{d y}{d x} - 2 y = x y^{4}, y (0) = - 2

(\frac{2 y}{x} + 2 x) + (2 ln (x) - 3) (\frac{d y}{d x}) = 0

d er i v a t i v e \frac{1}{4 ^{x}}