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Instructions: Show all necessary work, express all answers in simplest non-decimal form; no points for bald answers! 1. State the order of each ordinary differential equation, as well as its type (as linear (L) or non-linear (NL)) 10 1-10pts Order Type Order Type a)(y-x)y, y-x 3 + xy = xy g)a+ (tanx)y cosx dx -x+2y ycosx 2. Verify that the function is a solution of the given differential equation. (a) y,-3y = 0; y = 2e3x dx y ae41-be-z , a, b constant dt 3. Determine the region in the ry-plane for which the ODE would have a unique solution through a point (xa yo). (b)y 2y-x 4. (i) Determine the region in the xy-plane for which the ODE would have a unique solution through a point ( Yo). (ii) Determine whether the given function is a solution of the differential equation. (a) (y-x)y = y-x+8; y=x+4G+2 ecos32x: y*- j(sin2x-sin 2) 5. (i) Verify that the function is a solution of the given differential equation. (ii) Find the solution of the given IVP from the indicated family of solutions. (a) y, + 2xy2 =0, yG)--4 ; y=1/ (r2 + c) (c) y +25y 0, y (0)-2, y(0) 3 y csin5x c cos5x (e) y-4y + 4y = 0, y(0) = 1, y(0) = 2; y = c1e2x + C2Xe2x dx ae +3be2 a, b constant dt
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