Thread: Separable Differential Equations-Please help!

I've got a few of these separable differential questions to ask. The thing I'm most confused about is what to do with the constant when you are given what y and x equal.

Solve each of the initial value problems-

1) e^x.y.(dy/dx) = 1 y = 0 when x = 0

2) xy.(dy/dx) = 1 + y^2 y = 0 when x = 2

Find the particular solution-

3) dy/dx = (1/3) + y^2 y = 1/2 when x = pi/4

4) dh/dt = 2h(3-h) where h = 1 when t = 0

Also these ones.

Solve:

5) (x^2 + 1).(dy/dx) + y^2 + 1 = 0

Sorry about all the questions, but im really confused with these

Originally Posted by hats_06

I've got a few of these separable differential questions to ask. The thing I'm most confused about is what to do with the constant when you are given what y and x equal.

Solve each of the initial value problems-

1) e^x.y.(dy/dx) = 1 y = 0 when x = 0

2) xy.(dy/dx) = 1 + y^2 y = 0 when x = 2

Find the particular solution-

3) dy/dx = (1/3) + y^2 y = 1/2 when x = pi/4

4) dh/dt = 2h(3-h) where h = 1 when t = 0

Also these ones.

Solve:

5) (x^2 + 1).(dy/dx) + y^2 + 1 = 0

Sorry about all the questions, but im really confused with these

How much experience do you actually have in solving differential equations? I'll do one.

2) xy.(dy/dx) = 1 + y^2 y = 0 when x = 2.





.

Substitute y = 0 when x = 2: .

Therefore:





.

Therefore y = .....

Thanks for that!