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Can i have the solution for this exact equation(differential equation), (2xy-y)dx + (x²+x)dy=0 ....?
This is the final answer. y(x-1)³=cx
I need the solution.. Thank you.
1 Answer
- hfshawLv 71 decade agoFavorite Answer
The solution you provided is incorrect, as you can verify by taking the derivative, plugging it into the differential equation and seeing if the equation is satisfied. (It's not.) The correct solution is given below. The solution contains a factor of (x+1)^3, not (x-1)^3, as you have written.
This is a separable equation:
(2xy-y)dx + (x^2 + x)dy
y(1-2x)dx = (x^2+x)dy
(1-2x)/(x^2 + x) dx = dy/y
Expand the left hand side using partial fractions:
(1/x - 3/(x+1)) dx = dy/y
ln(x) - 3*ln(x+1) = ln(y/c)
where c is a constant of integration.
ln(x/(x+1)^3) = ln(y/c)
y = c*x/(x+1)^3
