differentiate:xy'+2y=x^2

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differentiate:xy'+2y=x^2

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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I have one solution: c/x^2+x^2/4; but confusion, could any one help me
define for me "differentiate" as it applies to this problem please...
...ordinary differential equation....right?

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Other answers:

yes
if I recall correctly, that means your trying to find the original function that this was derived from correct?
yeah
the only method I remember off hand is the seperation of variables.... have you tried that yet?
i think seperation variable is not correct for this equation
youre probably right...step me through what youve done already
i apply bernoulli's equa.
y' + P(x)y = Q(x)y^n.. that one?
y'+p(x)y=r(x)
hmmm.... I havent had much practice with ode's .... maybe someone smarter will come along :)
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.
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...
c/x^2+x^2/4 i have already mention above
is it correct?
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..

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