MATH 202 Questions, Fall 1998

7. By the substitution method a solution of the boundary-value problem of the differential equation y" + 2y(y')? =O y(1) = 0, (4) = 3 satisfies (a) y(—2/3) = 1. (b) y(—2/3) = 2 (©) v(-2/8) = =I. (a) y(-2/3) = —2. (c) y(-2/8) = 0. 8. ‘The function k(y) wilh (0) = 0 thal makes the diflereutial equation {e?¥ +- h(y)|dx - [e714 +e nye”|dy = 0 exach must satisfy (a) h(1) = —1. (b) h(-1) = 1. (c) h(1) =1. (d) h(-1) = 1. (e) none of the above. 9. The solution of the boundary-value problem y+ 4y = 3sin2s, y(0) = 1,y(r/4) =—-1 satisfies (a) y(m) = -1 + V2. (b) y(—m/4) = 1. (c) y(-1/2) = -1—m. (d) y(/2) = -1- V2. (e) none of the above. 10. By using the change of variable y(x) = «7 ?u(x) Une diflercutial equa- tion . sy" -+ Ty’ | cy = 0 changes to a (a) Cauchy-[yuler differential equation. (b) Bessel differential equation with v = 6. (c) Bessel differential equation with v = 3. (d) Bessel differential equation with v = 7. (e) none of the above. 6 Lt. If as) = ‘eT eos 7dr}, then G(2) is equal to (a) 3/20. (b) 3/10. (c) 7/20. (a) -1/2. (c) none of the above. 12. if F(s) = L{(t- Let - 1}, then F(3) is equal to (a) 3e-2/8, (b) 3073/8. (c) °9/3. (a) 1/3. (e) none of the above. 13.’ The solution to the initial-value problem iy’ —y' =t?, (0) =y'(0) = 0, y"(0) = 1 satis fics (a) y(—2) = —2/8. (b) y(2) = 13/3. (c) y) = 7/6. (d) x(-1) = -1/6. (c) y(3) = -27/2. 14. If the sysbem z'(t) —Gx-3y = 8e! 4c! y(t) — 2n-y satisfies x(0) = —1 and (0) = 0, then (a) y(t) = (e' — e%)/3. (b) a(t) = et — 2c". (a) x(t) = —2e! + e. (e) none of the above. 15. “The solution of the integro-diflerential equation t (t= cost + | costf(L—7)dr f(0) =0 satisfies (a) (2) =3. (b) (2) =4. Il (c) £(2) (a) f(2) =x. 3 (c) f(2) = 5. 2. 1 1G. ‘Phe indicial roots of the differential equation (a) 5/2, 1/2. (b) 5/2, 5/2. (c) 3/2, -1/2. (d) 3/2, 1/2. (e) 5/2, -1/2. xy" ~ zy! — (2? +: 5/4)y =0 are 9 3%