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i am having trouble finding the general solution for the given homogeneous equation:

x

which i made into

x

i turned it into the following:

(2y

then i used substitution of y = xv and got

(2(xv)

then i turned this into the following ... i think this may be the part i did wrong

(2v

then the integrating factor was

1/x(2v

so...

dx/x - dv/(2v

i am stuck here. i know the first part is ln x, but I'm not sure if the second part is [ln (2v

y(x) = x + Cx

please help. thx.

x

^{2}yy' = (2y^{2}- x^{2})which i made into

x

^{2}dy = (2y^{2}- x^{2}) dxi turned it into the following:

(2y

^{2}- x^{2}) dx - x^{2}dy = 0then i used substitution of y = xv and got

(2(xv)

^{2}- x^{2}- x^{2}v) dx - x^{3}dv = 0then i turned this into the following ... i think this may be the part i did wrong

(2v

^{2}- 1 - v) dx - x dv = 0then the integrating factor was

1/x(2v

^{2}- 1 - v)so...

dx/x - dv/(2v

^{2}- 1 - v) = 0i am stuck here. i know the first part is ln x, but I'm not sure if the second part is [ln (2v

^{2}- 1 - v)]/(4v - 1)...if this part is right then i am stuck again here. i don't know how to get to the final solution which isy(x) = x + Cx

^{4}/1 - 2Cx^{3}please help. thx.

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