Find the Laplace transform of e ^ (3t) - 2e ^ (-2t) + sin 2t + cos 3t + sinh(3t) - 2cosh(4t) + 9

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on Jan 25, 2025 at 11:10 pm



You asked:

Find the laplace transform of e3t−2e−(2t)+sin⁡(2t)+cos⁡(3t)+sinh⁡(3t)−2cosh⁡(4t)+9{e}^{3 t} - 2 {e}^{-\left( 2 t \right)} + \sin\left( 2 t \right) + \cos\left( 3 t \right) + \sinh\left( 3 t \right) - 2 \cosh\left( 4 t \right) + 9

MathBot Answer:

Lt{e3t+sin⁡(2t)+cos⁡(3t)+sinh⁡(3t)−2cosh⁡(4t)+9−2e−2t}(s)=ss2+9−2ss2−16+2s2+4+3s2−9−2s+2+1s−3+9s\mathcal{L}_{t}\left\{e^{3 t} + \sin{\left(2 t \right)} + \cos{\left(3 t \right)} + \sinh{\left(3 t \right)} - 2 \cosh{\left(4 t \right)} + 9 - 2 e^{- 2 t}\right\}(s) = \frac{s}{s^{2} + 9} - \frac{2 s}{s^{2} - 16} + \frac{2}{s^{2} + 4} + \frac{3}{s^{2} - 9} - \frac{2}{s + 2} + \frac{1}{s - 3} + \frac{9}{s}Converges for Re(s)>4Re(s) > 4

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