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Let y = y(x) be the solution of the differential equation (y² - x) dy/dx = 1 with y(0) = 1. The solution curve meets the x-axis at a point; find the x-coordinate (abscissa) of that point.
- 2 + e
- 2
- 2 - e
- -e
Correct answer: 2 - e
Solution
Solving the linear ODE dx/dy + x = y² gives x = y² - 2y + 2 + Ce^(-y); using y(0)=1 (point (0,1)) gives C = -e, so at y = 0, x = 2 - e.
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