- #1
JoeTrumpet
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Homework Statement
Solve this differential equation:
(y^2 +1)*dx + (2xy + 1)*dy = 0
Homework Equations
dy/dx + P(x)*y = Q(x)
u(x) = e^(integral of P(x)dx)
(d/dx)(u(x)*y) = Q(x)*u(x)
y = (integral of (Q(x)*u(x)dx))/(u(x)
The Attempt at a Solution
I tried dividing by dx then distributing and rearranging to get it into the right form, but run into problems:
y^2 + 1 + 2xy*dy/dx + dy/dx = 0
dy/dx + y/2x = (-1/(2xy))(dy/dx) -1/(2xy)
this is the closest I could get it to the right form. It would give me u(x) = x^(1/2), but I wouldn't be able to integrate the right side as it would have both x and y. Is there a way to get past this, or did I just rearrange poorly? I just integrated it anyway and the part that was integrated with respect to x I held y as constant, and vice versa, but I'm sure it's wrong so I won't show how I did that. This is for a calc II class so it should be doable without any advanced tricks.
thanks!