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EXERCISES 3: LINEAR EQUATIONS Solve each differential equation. 1. dy 1 yx dx x 2. dy 1 y ex dx x 3. dy y e3x dx 4. dr r tan sec d 5. ( x 2 1) dy xy x dx 6. dy y 4e x , y(0)=4 dx 7. dy 1 3x 2 y x3 , y(0)=2 dx e 8. dy y cos x 4 , y , x 0 dx x x 2 9. (e x 1) dy e x y x, dx y (0) 1 10. x dy y x 2e x , dx 11. t 3 dx 3t 2 x t , x(2) 0 dt y (1) e 1 ANSWERS: 1 2 c x 3 x x e c 2. y e x x x 1 3x 3. y e ce x 2 4. r sin c cos 1. y 5. y 1 c( x 2 1) 6. y 4e x ( x 1) 12 7. y 2e x xe x 1 8. y (1 sin x) x x2 2 9. y x x 2(e 1) e 1 3 10. y xex x 1 2 11. x 3 2t t 3