How many straight lines satisfy the differential equation dy/dx + x*(dy/dx)² - y = 0?

Correct answer: 2

Solution

Substituting y = mx + c gives m + x*m² - mx - c = 0; matching coefficients gives m = 0, c = 0 (y = 0) and m = 1, c = 1 (y = x + 1) — two lines.

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