# Recent questions in Laplace transform

Laplace transform

### Inverse Laplace transformation $$(s^2 + s)/(s^2 +1)(s^2 + 2s + 2)$$

Laplace transform

### Use the table of Laplace transform and properties to obtain the Laplace transform of the following functions. Specify which transform pair or property is used and write in the simplest form. a) $$x(t)=\cos(3t)$$ b)$$y(t)=t \cos(3t)$$ c) $$z(t)=e^{-2t}\left[t \cos (3t)\right]$$ d) $$x(t)=3 \cos(2t)+5 \sin(8t)$$ e) $$y(t)=t^3+3t^2$$ f) $$z(t)=t^4e^{-2t}$$

Laplace transform

### Explain why the function is discontinuous at the given number a. Sketch the graph of the function. $$f(x) = \left\{\frac{1}{x+2}\right\}$$ if $$x \neq -2$$ $$a= -2$$ 1 if $$x = -2$$

Laplace transform

### Use the Laplace transform to solve the given initial-value problem. $$dy/dt-y=z,\ y(0)=0$$

Laplace transform

### Find the Laplace transform of the function $$L\left\{f^{(9)}(t)\right\}$$

Laplace transform

### Use Theorem 7.4.3 to find the Laplace transform F(s) of the given periodic function. F(s)=?

Laplace transform

### Determine $$L^{-1}\left[\frac{(s-4)e^{-3s}}{s^2-4s+5}\right]$$

Laplace transform

### Obtain the Laplace Transform of $$L\left\{e^{-2x}+4e^{-3x}\right\}$$

Laplace transform

### $$\displaystyle{y}'={6}\frac{{x}^{{2}}}{{{2}{y}+{\cos{{y}}}}}$$

Laplace transform

### Find the Laplace transforms of the given functions. $$f{{\left({t}\right)}}={6}{e}^{{-{5}{t}}}+{e}^{{{3}{t}}}+{5}{t}^{{{3}}}-{9}$$

Laplace transform

### $$L^{-1}\bigg(\frac{5}{s^{2}(s^{2}-4s+5)}\bigg)=5\int_{0}^{\infty}(t-T)e^{2T}\sin 2T\ dT$$ Select one: True or False

Laplace transform

### Solve the following IVP using Laplace Transform $$y′′+3y′+2y=e^{-t}, y(0)=0 y′(0)=0$$

Laplace transform

### How to solve for third order differential equation of $$y"'-7y'+6y =2 \sin (t)$$ using Method of Laplace Transform when $$y(0)=0, y'(0)=0, y"(0)=0$$? Step by step

Laplace transform

### Use the appropriate algebra and Table of Laplace's Transform to find the given inverse Laplace transform. $$L^{-1}\left\{\frac{1}{(s-1)^2}-\frac{120}{(s+3)^6}\right\}$$

Laplace transform

### Determine the Laplace transform of the given function f. $$f(t)=(t -1)^2 u_2(t)$$

Laplace transform

### use the Laplace transform to solve the initial value problem. $$y"-3y'+2y=\begin{cases}0&0\leq t<1\\1&1\leq t<2\\ -1&t\geq2\end{cases}$$ $$y(0)=-3$$ $$y'(0)=1$$

Laplace transform

### Find the laplace transform by definition. a) $$\displaystyle{L}{\left\lbrace{2}\right\rbrace}$$ b) $$\displaystyle{L}{\left\lbrace{e}^{{{2}{t}}}\right\rbrace}$$ c) $$\displaystyle{L}{\left[{e}^{{-{3}{t}}}\right]}$$

Laplace transform

### Find the solution of the initial value problem given below by Laplace transform $$y'-y=t e^t \sin t$$ $$y(0)=0$$

Laplace transform