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Solve the following homogeneous differential equations.
6. The slope of the tangent to a curve at any point (x, y) on it is given by (y3 − 2 yx2 )dx +(2xy2 − x3 ) dy = 0 and the curve passes through (1, 2). Find the equation of the curve.
7. An electric manufacturing company makes small household switches. The company estimates the marginal revenue function for these switches to be (x2 + y2 )dy = xydx where x represents the number of units (in thousands). What is the total revenue function?
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