Wribreeminsl

2021-09-08

Find $L\left\{9+6t\right\}$
$L\left\{k\right\}=\frac{k}{s}$
$L\left\{t\right\}=\frac{1}{{s}^{2}}$

doplovif

Step 1
Given
The given expression is $L\left\{9+6t\right\}$
Apply Laplace transform formula
$L\left\{k\right\}=\frac{k}{s}$ , where k = constant
$L\left\{t\right\}=\frac{1}{{s}^{2}}$
Step 2
Calculation
$L\left\{9+6t\right\}$
=$L\left\{9\right\}+L\left\{6t\right\}$
$=\frac{9}{s}+\frac{6}{{s}^{2}}$
$=\frac{9s+6}{{s}^{2}}$
$=\frac{3\left(3s+2\right)}{{s}^{2}}$
Hence, $L\left\{9+6t\right\}=\frac{3\left(3s+2\right)}{{s}^{2}}$

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