anonymous
  • anonymous
differentiate:xy'+2y=x^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
I have one solution: c/x^2+x^2/4; but confusion, could any one help me
amistre64
  • amistre64
define for me "differentiate" as it applies to this problem please...
amistre64
  • amistre64
...ordinary differential equation....right?

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anonymous
  • anonymous
yes
amistre64
  • amistre64
if I recall correctly, that means your trying to find the original function that this was derived from correct?
anonymous
  • anonymous
yeah
amistre64
  • amistre64
the only method I remember off hand is the seperation of variables.... have you tried that yet?
anonymous
  • anonymous
i think seperation variable is not correct for this equation
amistre64
  • amistre64
youre probably right...step me through what youve done already
anonymous
  • anonymous
i apply bernoulli's equa.
amistre64
  • amistre64
y' + P(x)y = Q(x)y^n.. that one?
anonymous
  • anonymous
y'+p(x)y=r(x)
amistre64
  • amistre64
hmmm.... I havent had much practice with ode's .... maybe someone smarter will come along :)
anonymous
  • 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.
anonymous
  • 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...
anonymous
  • anonymous
c/x^2+x^2/4 i have already mention above
anonymous
  • anonymous
is it correct?
anonymous
  • 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..

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