Differential Equation general solution

[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

 

[pizzasky]

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)?

 

[Natasha1]

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)?

For part 3) I suppose any of the two

 

[HallsofIvy]

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)

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.

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

Could someone help me on this one

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.

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

Well, what happens if you set x= pi?

Could someone help me on this one please