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Suppose you want to find an equation for a curve that passes through the point (1, 2) and whose slope at any point (x,y) is 2x^3/y. You'd solve the differential equation dy/dx = 2x^3/y with initial condition y(1) = 2. Solving this differential equation with initial condition, you get:

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y = sqrt(4x^6 + 4)

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