Linear and Bernoulli First Order

[darkmagic]

1. The problem statement.

1. http://img194.imageshack.us/img194/3815/linear.png

2. http://img25.imageshack.us/img25/1543/bernoulli1.jpg

3. http://img23.imageshack.us/img23/7991/bernoulli2.jpg

2.Relevant equations

Problem 1 is Linear Differential Equation and Problems 2 and 3 are Bernoulli's D.E.

LDE is given by: dy/dx + yP(x) = Q(x)
BDE is given by: dy/dx + yP(x) = Q(x)y^n

The Attempt at a Solution

On those three equations, I'm trying to make the equations as exactly to the format on the LDE and BDE. However, I cannot get P(x) and Q(x) on no.1. The y is always y^3. In no.2, there will be Q(x)y^n and there is no y. In no.3, I solved that. However, that problem is BDE and I solved it using LDE with dx/dy. Do you think there is something wrong with the equation?

Thank you.

 

[darkmagic]

I think I solved the three equations. There's something wrong with those equations. The first problem can be solved by using Bernoulli but it is under the linear problem set. I got the same answer exactly as the provided answer. The second problem is Bernoulli. I modified the equation and when I solved it, I got the same answer exactly as the provided answer. The equation goes 2x^3y'=y(y^2+3x^2). The third problem is the same as the first. Instead of Bernoulli, it is solvable using Linear. Anyway, thank you.