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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

### Solve the linear equations by considering y as a function of x, that is, y = y(x). $$y'+2y=4$$

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

### Solve differential equation $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\left({x}+{y}+{1}\right)}^{{2}}-{\left({x}+{y}-{1}\right)}^{{2}}$$

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