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Home Q & A Board Science-Related Homework Help Mathematics
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nvaldivi2 nvaldivi2
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11 years ago
I use substitution y=vx , but I get stucked at (2+2v)/(v^2+2v) dv = 1/x dx.

Thanks for the help!!!
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wrote...
#1
11 years ago
U R right.
But you get sucked because you did not notice that  (2+2v)/(v^2+2v)  = 2/v after simplication.
Simple algebra!!!!
wrote...
#2
11 years ago
its a homogenous D.E.
it can be written as y'=(3y^2+4xy)/(2x^2+2xy).

Now on RHS divide numerator and denominator by highest power of x present in the equation i.e. x^2. We get
y'=[3(y/x)^2+4(y/x)]/[2+2(y/x).

Now substitute y/x =t
on differtiating both sides we get.
y'=t+xt'

now overall eq becomes:
t+xt' = (3t^2+4t)/(2+2t)

by variable seperable:

(t^2+2t)/(2+2t) dt = (dx)/x
integrate both sides to get anwser
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