Find the general solution to the differential equation x^2 dy dx + 2xy = 2x + 1

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

Find the general solution to the differential equation x2dydx+2xy=2x+1x^2 \frac{dy}{dx} + 2xy = 2x + 1 (1) Find the general solution to the differential equation x2dydx+2xy=2x+1x^2 \frac{dy}{dx} + 2xy = 2x + 1 (2) Find the three particular solutions which pass through the points with coordinates (−12,0)(-\frac{1}{2}, 0), (−12,3)(-\frac{1}{2}, 3) and (−12,19)(-\frac{1}{2}, 19) respectively and sketch their solution curves for x<0x < 0.

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