3 The equation of the curve, the slope of which is 4-2x, and which passes through the point (2,6) is_ -- a. y=2x - x² + 2 b. y=4x - x2 c. y=4x - x2 + 2 d. y=x - x2+1 e. y=x - x2 4 x2y" + 2xy` =1 is a...

Extracted text: 3 The equation of the curve, the slope of which is 4-2x, and which passes through the point (2,6) is_ -- a. y=2x - x² + 2 b. y=4x - x2 c. y=4x - x2 + 2 d. y=x - x2+1 e. y=x - x2 4 x2y" + 2xy` =1 is a DE in second order special case. The integrating factor is a. X b. x 2 C. x 2 d. x -1


Extracted text: 1. The solution to the non-homogeneous DE (D? + 2D +5) y = 3 e* sin x - 10 is a. e* cos x- 2 + e* (a cos 2x + C2 sin 2x) b. e* sin x - 2 + e* (q cos 2x + Cz sin 2x) c. ex sin 2x - 10 + e* (a cos 2x + c2 sin 2x) d. e* sin 2x - 2+ e* (c, cos x + cz sin x) e. e* sin x + 2 + e* (a cos x + C2 sin x) The solution to the non-homogeneous DE y - 5y' +6y = 2x + 3 is a. Ae3x + Be* + 1/3 x + 7/9 b. Aө3x + Be3x +2/3х+4/3 C. Ae* + Be* + 1/3 x + 7/9 d. Ae + Bex + 1/3 x + 7/9 e. Ae2* + Be2x + 2/3 x + 4/3