Simple differential equation in calc 2.?

Question

Ok, I'm lost on this section. This is an unassigned HW question I think would help me to figure out if I could see how to do this the question is to find a general form for x'-y^2=2x and then to show it is really the answer.
I can't figure this out, any help?

Yes you are correct, that would be another way to write it.

Answer 1

Do you mean dx/dy - y² = 2x or is x a function?


Doug

Answer 2

If you dont mind, I will change x and y, since most times x is the independant variable and y, the dependant one.

y' - x^2 = 2y

y' - 2y = x^2

This is a non homogen (?) differential equation. Im sorry, Im not a native speaker, but I hope that you will understand what I mean.

The steps are these ones:

1) solve the homogen differential equation, this is

y' - 2y = 0

This is done this way:

dy/dx = 2y

dy/y = 2dx

Just integrate:

ln y = 2 x+ c

And y = e^(2x+c) = (e^(2x)) e^c

y = A e^(2x)

2) find a particular solution, x = k is usually a solution.

y' - 2y = x^2

y could be a polynomial in this case.

y = mx^2 + nx + p

y' = 2mx + n

Try and see if it functions.

3) Add both solutions

Then, using the initial conditions, calculate A

Ana

Ana

Answer 3

dx/dy - y^2 = 2x multiply out with the help of dy so as that dx - y^2dy = 2xdy combine out the two sides I[dx] - I[y^2dy] = 2xI[dy] + consistent x - (a million/3)y^3 = 2xy + consistent 3x - y^3 = 6xy + consistent Is the what you're in seek of for?

Answer 4

I don't know the answer to that. My number is 4.