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romanna [79]
3 years ago
10

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

Mathematics
1 answer:
Alex_Xolod [135]3 years ago
4 0

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}.

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Please help with question
Step2247 [10]
To solve this problem you must apply the proccedure below:

 1. Let's call:

 x: hot dogs.
 y: hamburguers.

 2. Then, you must make a system of equations, as below:

 5x+4y=12.25  (i)
 4x+5y=12.50  (ii)

 3. Now, you can solve the system of equation as below:

 5x+4y=12.25
 x=(12.25-4y)/5

 4x+5y=12.50
 4((12.25-4y)/5)+5y=12.50
 y=1.5

 4x+5y=12.50
 4x+5(1.5)=12.50
 x=1.25

 4. Therefore, the answer is:

 The cost of one hot dog is $1.25 and the cost of one hamburguer is $1.50
 
8 0
3 years ago
Given the Arithmetic sequence A1,A2,A3,A4 20, 27, 34, 41 What is the value of A17 ?
Sedaia [141]
A17=132
27-20=7 and 34-27=7 so they're adding 7 to each term
A17-A4=13 terms between the last one you're given and the one you're trying to find.
13*7=91
91+41=132
5 0
3 years ago
What are the coordinates of the point which would complete the rectangle shown above?
Strike441 [17]

Answer:

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Step-by-step explanation:

8 0
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polet [3.4K]

Answer:

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Step-by-step explanation:

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pychu [463]
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120 inches is greater that 100 inches.
6 0
4 years ago
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