Question

Find the Laplace transform of √te^3t​

Answer 1

Answer:

✓

52

Step-by-step explanation:

78(8+8)u×7@ ⁷⁶⁸;’¡

ans = √2335

Answer 2

Concept

Recall the rule which will use to solve further

Transform rule:

If L{f(t)}=F(s) then L{$e^{a t}$ f(t)} = F(s-a)

Given

The expression $\sqrt{t}e^{3t$

To find

We have to find the  Laplace transform of this given expression.

Solution

Apply the transform rule to solve the Laplace transformation.

$L\{\sqrt{t}e^{3t}\}=L\{\sqrt{t}\}(s-3)$

              $= \{\frac{\sqrt{\pi}}{2 s^{\frac{3}{2}}}\}(s-3)$

              $=\frac{\sqrt{\pi}}{2(s-3)^{\frac{3}{2}}}$

Hence the final value is $\frac{\sqrt{\pi}}{2(s-3)^{\frac{3}{2}}}$.