I am trying to solve this equation for 2 days and I can't do it.... I solved it but wolfram alpha gives different answers. Please help me to find my mistake ;)

Attachment 30947 - this is my solution. - Wolfram alpha answer

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- May 17th 2014, 08:11 AMdarjiaus7Can't find my mistake in dif equation
I am trying to solve this equation for 2 days and I can't do it.... I solved it but wolfram alpha gives different answers. Please help me to find my mistake ;)

Attachment 30947 - this is my solution. - Wolfram alpha answer - May 17th 2014, 08:29 AMprasumRe: Can't find my mistake in dif equation
in wolfram alpha input u have given rhs as -2/x^3 while in ur soln u have computed for -2/x^2

- May 17th 2014, 08:43 AMSlipEternalRe: Can't find my mistake in dif equation

The integrating factor is , so multiply both sides by that:

Integrating both sides:

Multiply both sides by :

Integrate both sides:

Fold the into a single constant:

When you entered the problem into WolframAlpha, you entered . Notice the RHS of that differential equation has in the denominator. Your original problem has in the denominator. - May 17th 2014, 08:53 AMHallsofIvyRe: Can't find my mistake in dif equation
You are correct that the general solution to the associated homogeneous equation is but you are doing the "variation of parameters" incorrectly.

Yes, we look for a solution to the entire equation of the form , allowing the "parameters", and to "vary".

Then we have . We simplify the equation (there are many different possible functions for and ) by requiring that leaving . Differentiating again, and now the differential equation becomes .

There is your error- you have, although you don't say how you arrived at it, on the left rather than . - May 17th 2014, 09:00 AMdarjiaus7Re: Can't find my mistake in dif equation
Can you explaint this part? And why you wrote y' instead of 2y' and got right answer?

- May 17th 2014, 09:21 AMdarjiaus7Re: Can't find my mistake in dif equation
Sorry I can't understand integrating factor method, can you say where is error in my solution? ;/

- May 17th 2014, 09:45 AMSlipEternalRe: Can't find my mistake in dif equation
- May 17th 2014, 11:20 PMdarjiaus7Re: Can't find my mistake in dif equation
Ok forget about my solution ;) Now can you explain how became

- May 18th 2014, 12:30 AMprasumRe: Can't find my mistake in dif equation
this is easy use product rule of differentiation d(fg)=fd(g)+gd(f)

here f=1/(x^2) and g=y'