Author Topic: tut5103 quiz1  (Read 611 times)

yangyiq5

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tut5103 quiz1
« on: September 27, 2019, 02:03:56 PM »
y’ = (x^2+3x^2)/(2xy)

sol:
y’ = (x^2+3x^2)/(2xy) = x/2y + 3y/2x = 1/2(y/x) ^ (-1) +3/2(y/x)
this equation is homogenous
u = y/x   y = ux
y’ = du/dx*x +u
du/dx*x +u = 1/2u^ (-1) +3/2u
separable
(2u/(1+u^2)) du = 1/x dx
Integral both sides
ln|1+u^2| = ln|x|
1+u^2 = cx
y^2/x^2 +1 = cx
y^2+x^2-cx^3=0