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2 years ago

12

Help please!! Will mark brainstest!!

1 answer:

cluponka [151]2 years ago

6 0

The correct answer is letter B

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Find a solution to y'(t) = te^-t satisfying the condition y(1) = 1.

Alex_Xolod [135]

Answer:

$y=-e^{-t}(t+1)+1+\frac{2}{e}$

Step-by-step explanation:

The given differential equation is

$y'(t)=te^{-t}$

It can be written as

$\frac{dy}{dt}=te^{-t}$

$dy=te^{-t}dt$

Integrate both sides.

$\int dy=\int te^{-t}dt$

Apply ILATE rule on right side. Here, t is first function and $e^{-t}$ is the second function.

$y=t\int e^{-t}-\int (\frac{d}{dt}t\int e^{-t})$

$y=-te^{-t}-\int (1\times (-e^{-t}))$ $\int e^{-x}=-e^{-x}+C$

$y=-te^{-t}+\int e^{-t}$

$y=-te^{-t}-e^{-t}+C$ .... (1)

Initial condition is y(1) = 1. It means at t=1 the value of y is 1.

$1=-(1)e^{-t}-e^{-(1)}+C$

$1=-e^{-1}-e^{-1}+C$

$1=-2e^{-1}+C$

$1=-\frac{2}{e}+C$

Add $\frac{2}{e}$ on both sides.

$1+\frac{2}{e}=C$

Substitute the value of C in equation (1).

$y=-te^{-t}-e^{-t}+1+\frac{2}{e}$

$y=-e^{-t}(t+1)+1+\frac{2}{e}$

Therefore, the solution of given initial value problem is $y=-e^{-t}(t+1)+1+\frac{2}{e}$ .

4 0

3 years ago

I need help with These

Kamila [148]

I'm not sure about d.

This was what I could come up with.

6 0

3 years ago

What is the solution to the equation?<br> 2<br> a+53 =<br> =9

Andre45 [30]

Answer:

-22

Step-by-step explanation:

8 0

3 years ago

60 pts!!! HELP Find the inverse of the function f(x)= 4/9 x-4<br> show work

earnstyle [38]

Answer:

Inverse Function: f^-1(x) = 9/4x + 9

Step-by-step explanation:

To find the inverse function we can interchange the position of the variables x and y, and then solve for y;

y = 4/9x - 4 => x = 4/9y - 4,

x = 4/9y - 4,

4/9y = x + 4,

y = 9/4x + 9/4(4),

y = 9/4x + 9/ f^-1(x) = 9/4x + 9

6 0

3 years ago

How can we get System B from System A?<br><br><br> And are they equivalent?

Aliun [14]

What? Where’s the question 11

8 0

3 years ago