2 years ago

Solve the equation y′ + 3y = t + e^(−2t).

1 answer:

4 0

Hello,

I am going to remember:

y'+3y=0==>y=C*e^(-3t)

y'=C'*e^(-3t)-3C*e^(-3t)

y'+3y=C'*e^(-3t)-3Ce^(-3t)+3C*e^(-3t)=C'*e^(-3t) = t+e^(-2t)
==>C'=(t+e^(-2t))/e^(-3t)=t*e^(3t)+e^t
==>C=e^t+t*e^(3t) /3-e^(3t)/9

==>y= (e^t+t*e^(3t)/3-e^(3t)/9)*e^(-3t)+D
==>y=e^(-2t)+t/3-1/9+D
==>y=e^(-2t)+t/3+k

You might be interested in

The area of a closet is 100 square feet. Write the number in exponent form and in word form

wlad13 [49]

Exponent form is 10^2 square ft and word form is one hundred square feet

8 0

1 year ago

Read 2 more answers

Which equation represents a line that passes through (4, left-parenthesis 4, StartFraction one-third EndFraction right-parenthes

lina2011 [118]

Answer:

$y-\frac{1}{3}=\frac{3}{4}(x-4)$

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

In this problem we have

$(x_1,y_1)=(4,\frac{1}{3})$

$m=\frac{3}{4}$

substitute the given values

$y-\frac{1}{3}=\frac{3}{4}(x-4)$

therefore

y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)

6 0

1 year ago

Read 2 more answers

How could Brent use a rectangle to model the factors of x2 – 7x + 6?

Crank

<span> He could draw a diagram of a rectangle with dimensions x – 1 and x – 6 and then show the area is equivalent to the sum of x2, –x, –6x, and 6.</span>

6 0

2 years ago

Read 2 more answers

Mya is doing a 45-minute cardio workout. She has completed 4 5 of the workout. In how many minutes will her workout be done?

Alika [10]

Answer:

9 minutes

Step-by-step explanation:

45/5 equals 9

6 0

2 years ago

Jackson owes his sister Monica $15. Monica has a $10 bill in her pocket. Explain the meaning of zero in this situation .?