Input Differential

help on my differential equations homework?

I need to solve the homogeneous differential equation (x^2 + y^2)dx + 2xydy = 0.

Take the derivative of both:

(2x + 2yy’ ) + (2xy’ + 2y) =0
-We use the chain rule for y^2 to get 2yy’
-Use the product rule for 2xydy

Group all the (y’ ) together:
2yy’ + 2xy’ = -2x-2y

Factor out y’:
y’(2y+2x) = -2x-2y

Divide both sides by y’:

y’= (-2x-2y)/(2y + 2x)

Simplify if you want:

y’= 2(-x-y)/2(y + x)

y’ = (-x-y)/(y+x)

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