laplacetransform t+1^2

解答

拉普拉斯变换

t + 1^{2}

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

求解步骤

L {t + 1^{2}}

利用拉普拉斯变换的线性特性:

对于函数

f (t), g (t)

和常数

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

= L {t} + L {1^{2}}

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

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

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

\int_{0}^{11} 2 π y (\frac{y ^{2}}{2}) d y

in v erse l a pl a ce \frac{s}{( s + 4 )}

\frac{\partial}{\partial x} (x^{3} y^{5} - 2 x^{2} y + x)

\int_{0}^{2} (x^{3} - 3 x^{2} + 2 x) d x

\frac{d}{d x} (csc (\frac{ln ( x + 3 )}{x ^{2}}))