Help on Final Exam

[fbys294]

Please help, I'm not great at DE and my professor removes points for anything. If you can solve any of them it would help me pass.

1.) Solve the Initial Value Problem: y'= 4t+ty^2 / y+yt^2 , y(0)= -2


2.) Find the general solution to 2x^2 y'' + 7xy-3y = 0


3.) Use Laplace transforms to solve the IVP: y'''' - y=0 y(0)=0, y'(0)=0, y''(0)= -1, y'''(0)=0


4.) Find the general solution (2ye^(3xy) + 3xy^2 e^(3xy))dy + (3y^3 e^3xy -1)dx = 0

5.)Method of variation of parameters to find the solution: y'''-2y"-21y'-18y = 3+4e^-t

 

[mmm4444bot]

my professor removes points for anything

How many points will your professor remove for having somebody else complete your assignment?

The correct way to pass any course is to learn the material, plain and simple.

Waiting until the final exam to ask for help is not a good way to learn the material.

There's no shame in repeating a course. Just be mindful of your workload and resources. Plan accordingly.

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Anyhow, the way it works at this site is:

(1) You show some effort by telling us what you've thought about or tried thus far

(2) You explain what you're confused about or why you're stuck

(3) We provide guidance. We point out misconceptions. We correct errors

(4) You try again, and come back, if you still need help

Please read the post titled "Read Before Posting" for additional information on how to ask for help here. Thank you! :cool:

 

[fbys294]

Reply

What I mean is that they take off points for very small mistakes, and I need all the point. I can do the work but I don't like when I forget a 3 or a square and lose 4 points.

Is this correct.

Q: Use the method of undetermined coefficients to determine the general solution to the given differential equation: 4y''-11y'+6y = 10e^7t



4r² - 11r + 6 = 0
(2r - 3)(2r - 2) = 0


r = 3/2 = 1.5 and r = 1


yh = c₁e^1.5t + c₂e^t


To find the particulat part of the solution

We have p(t) = 10e^7t , therefore yp is of the form yp = Ae^7t :
4yp" - 11yp' + 6yp = (4(49A) - 11(7A) + 6A)e^7t = 125Ae^7t = 10e^7t

125A = 10 --> A = 10/125 = 0.08


The solution is:

y = yh + yp = c₁e^1.5t + c₂e^t + 0.08e^7t