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For the differential equation dy/dx + y*tan x = x*tan x + 1, which statement is correct?

1. The integral curves are given by y = x + c*cos x
2. The angle at which the integral curves cut the y-axis is pi/4
3. Tangents to all the integral curves at their points of intersection with the y-axis are parallel
4. none of these

Correct answer: The integral curves are given by y = x + c*cos x

Solution

With integrating factor sec x the equation integrates to y = x + c*cos x, so the family of integral curves is y = x + c*cos x.

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