# Differential Equation general solution

1. Apr 30, 2006

### Natasha1

1) I need to find the general solution, using the method of seperating the variables of the following diff Equ:

dy/dx = (2xcos x)/y where y>0

Is the answer = 2(cos x + xsinx)

2) If y = 2 when x = 0, find y in terms of x

Could someone help me on this one

3) Explain why your answer may not be used for x=pi. Comment in relation to the solution curve through (0,2).

Could someone help me on this one please

2. Apr 30, 2006

For part (1), you are on your way to getting the solution, but that is not the final answer. For one, where is your constant of integration? What expression is on the left hand side of your answer?

Part (2) just involves some substitution to enable you to evaluate the constant of integration for a particular solution.

For part (3), may I know whether we are supposed to use the expression for the general solution (part 1's answer) or that of the particular solution (part 2's answer)?

3. Apr 30, 2006

### Natasha1

For part 3) I suppose any of the two

4. Apr 30, 2006

### HallsofIvy

Staff Emeritus
Is what = 2(cos x+ x sin x)? Using integration by parts, the integral of 2xcos x dx is 2(cos x+ x sin x) but what happened to ydy?
And, as pizzasky said, you forgot the constant of integration.

Just do it! Replace y with 2 and x with 0 in your formula to determine what the constant of integration must be. Then solve for y.

Well, what happens if you set x= pi?