Find the equation of the solution to dydx=x6y through the point (x,y)=(1,3).

1 answer:

7 0

Separate the x's and y's.

dy/y = x^7 dx

Integrate both sides.

ln(abs(y)) = (x^8)/8 + C

To cancel the natural root, make both sides the power to e.

e^ln(abs(y)) = e^((x^8)/8 + C)

abs(y) = e^C * e^((x^8)/8)

y = + or - [e^C * e^((x^8)/8)

Now just bundle the + or - e^C into a single constant. We will call it A.

y = Ae^((x^8)/8)

Now plug in the point (1,3).

3 = Ae^((1^8)/8)

3 = Ae^(1/8)

A = 3/(e^(1/8))

So the equation is:

y = (3/(e^(1/8))*(e^((x^8)/8)

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Helpppppp please !!?

ch4aika [34]

Please refer to my image where it shows my work as I’m explaining.

Okay, for system 1:

1. I am using the elimination method to solve. So I check if all the terms are lined up and if any are the same. I found that 2X are common in both equations.

2. The goal is to “eliminate” the term hence the name. So I can choose to add or subtract. I chose subtraction because 2 - 2 equals 0 which is our goal. Solve for the rest of the terms. This will lead to getting y =4. Refer to image for the work.

3. Last step to to find the X value. We do this by picking any of the given equations,then substitute y with 4 and solve to eventually get x = 10. Refer to image for the work.

FOR SYSTEM 2:

1. Again, I am using the elimination method to solve. I noticed that NONE of the terms are in common so I will have to intervene. You can chose any term to create a match with but I chose Y since it was the one I could use the smallest number to multiply with. When multiplying, DONT just multiply Y, multiply ALL the terms in the equation or else everything will crash.

2. Now that I have terms in common I can choose to add or subtract. I chose subtraction because 2-2 equals zero which is what we want. Solve look at image for my process which lead to X = -8

3. Last step is to find the value of Y. Chose any of the given equations in system 2 then substitute x with -8. Refer to image to see process. It lead to y = 20

To check the validity of the answers, substitute the x and y values into both equations both side of the equal side should have the same number. Hope that helped!