MATH 3321 Quiz 4 1/31/17 1. y 0 = x2 (ex 2y) is (a) a linear equation. (b) a separable equation. (c) a Bernoulli equation. (d) a homogeneous equation. (e) none of the above. 2. xy 0 = ex y + 2x2 y 2 is (a) a linear equation. (b) a separable equation. (c) a Bernoulli equation. (d) a homogeneous equation. (e) none of the above. 3. y 3 y 0 = 2x2 y 4x3 is (a) a linear equation. (b) a separable equation. (c) a Bernoulli equation. (d) a homogeneous equation. (e) none of the above. 4. y 0 = xy 2 x y 2 + 1 is (a) a linear equation. (b) a separable equation. (c) a Bernoulli equation. (d) a homogeneous equation. (e) none of the above. 5. 3y 0 2x2 y 4 + 3x1 y = 0 is (a) a linear equation. (b) a separable equation. (c) a Bernoulli equation. (d) a homogeneous equation. (e) none of the above. 1 6. 2xyy 0 = 2y 2 + x2 cos(y/x) is (a) a linear equation. (b) a separable equation. (c) a Bernoulli equation. (d) a homogeneous equation. (e) none of the above. 7. The general solution of y 0 = 6x4 y 1/3 3y is: x 2 5 C x + 3 7 x 4 C y 2/3 = x5 + 2 7 x 4 C y 2/3 = x3 + 2 5 x C 1 y 2/3 = x3 + 2 15 x None of the above. (a) y 1/3 = (b) (c) (d) (e) 8. The general solution of xy 0 = 4x2 cos 2x + y is (a) y = 2x2 sin 2x + C/x (b) y = 2x cos 2x + Cx2 (c) y = 4x sin 2x + Cx (d) y = 2x sin 2x + Cx (e) None of the above. 9. The general solution of dy x3 + y 3 = is: dx xy 2 (a) y 2 = x2 ln x + Cx2 (b) y 3 = x ln x3 + Cx (c) y 3 = x3 ln x3 + Cx3 (d) y 2 = x2 ln x3 + Cx2 (e) None of the above. 2 10. The solution of the initial-value problem xey/x dy = x + yey/x , dx y(1) = 2 is: (a) y = x ln(e2 ) (b) y = x ln(ln x + e2 ) (c) y = ln(ln x + e2 ) ln(ln x + e2 ) x (e) None of the above. (d) y = 11. The solution of the initial-value problem 2y (a) y 2 = 2ex (b) y2 = 2 2 x 1 2 ex x 2 x1 1 (c) y = 2e dy = 2xy 2 + 2x y 2 1, y(1) = 1 is: dx x2 x (d) y 2 + 1 = e (e) None of the above. 12. The general solution of x2 y 0 + 2xy y 3 = 0 is: 4x Cx2 + 1 2 + Cx5 y2 = 3x 5x 2 y = 2 + Cx5 2 + Cx4 y2 = 5x None of the above. (a) y 2 = (b) (c) (d) (e) 3