Question

differentiate:xy'+2y=x^2

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

yes

Answer 5

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

Answer 6

yeah

Answer 7

the only method I remember off hand is the seperation of variables....

have you tried that yet?

Answer 8

i think seperation variable is not correct for this equation

Answer 9

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

Answer 10

i apply bernoulli's equa.

Answer 11

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

that one?

Answer 12

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

Answer 13

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

Answer 14

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.

Answer 15

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...

Answer 16

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

Answer 17

is it correct?

Answer 18

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..