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###### EXERCISES 12.3In Exercises 1-14 find the general solution of the differential equation. dy 1. &x +3y=0 2 dy dx (sinh x)y = 0 3 dy +2y = 4 dy dx dx 2y = * dy 5. &x-ay = f(x) 6. y + 2xy = 4x where f is continuous 1. y + 6xsy=xs Y33 (xy + 1) for x > 0 9.Y-y=1ze 10. d + ycosX = COsX 1L. dy + ytanx = tan x 12 dy ytan x = esin* dx dx for -w/2 < x < t/2 for -w/2 < x < t/2 13. dr {Y ~ sint? = 0 14. dy+y=tsint? + St dt for t > 0 for t > 0 In Exercises 15-18 fnd the particular

EXERCISES 12.3 In Exercises 1-14 find the general solution of the differential equation. dy 1. &x +3y=0 2 dy dx (sinh x)y = 0 3 dy +2y = 4 dy dx dx 2y = * dy 5. &x-ay = f(x) 6. y + 2xy = 4x where f is continuous 1. y + 6xsy=xs Y33 (xy + 1) for x > 0 9.Y-y=1ze 10. d + ycosX = COsX 1L. dy + ytanx = tan x 12 dy ytan x = esin* dx dx for -w/2 < x < t/2 for -w/2 < x < t/2 13. dr {Y ~ sint? = 0 14. dy+y=tsint? + St dt for t > 0 for t > 0 In Exercises 15-18 fnd the particular solution satisfying initial condition:

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