## anonymous 5 years ago differentiate:xy'+2y=x^2

1. anonymous

I have one solution: c/x^2+x^2/4; but confusion, could any one help me

2. amistre64

define for me "differentiate" as it applies to this problem please...

3. amistre64

...ordinary differential equation....right?

4. anonymous

yes

5. amistre64

if I recall correctly, that means your trying to find the original function that this was derived from correct?

6. anonymous

yeah

7. amistre64

the only method I remember off hand is the seperation of variables.... have you tried that yet?

8. anonymous

i think seperation variable is not correct for this equation

9. amistre64

youre probably right...step me through what youve done already

10. anonymous

i apply bernoulli's equa.

11. amistre64

y' + P(x)y = Q(x)y^n.. that one?

12. anonymous

y'+p(x)y=r(x)

13. amistre64

hmmm.... I havent had much practice with ode's .... maybe someone smarter will come along :)

14. anonymous

You can use the method: multiplying with an integrating factor. divide everything by x, so you'll have y'+2/x y=x. The integrating factor will then be: e^{2\int 1/x}=e^{2lnx}=e^{ln(x^2)}=x^2.

15. anonymous

Multiply both sides by the integrating factor x^2, then the left side will be (y*x^2)'. The right side is x^3. Then you integrate both sides, and gets y*x^2={1/4} *x^4+C Divide both sides of the equation by x^2 and you have the answer :) If you're not familiar with the method and wants a further explanation, just tell me...

16. anonymous

c/x^2+x^2/4 i have already mention above

17. anonymous

is it correct?

18. anonymous

Yes, it is correct. y=... , youre right. I only looked too much at the latter posts instead of where your answer was, I'm sorry for that..