MATH 361 EXAM 2, Fall 2001

Name:

1. Solve the equation: 2y′′ − 3y′ + y = 0,

Ans: .

2. Find the Wronskian of y_{1} = e^{−2t} and y_{2} = te^{−2t}:

Ans: .

3. Solve the equation: y′′ − 4y = 0, y(0) = 0 and y′(0) = 6.

Ans: .

4. Use Euler’s formula to write the given expression in the for a + ib.

a) e^{2−4i}

Ans: .

b) 2^{i}

Ans: .

5. Find the Wronskian of the two solutions of the differential equations: a) x^{2}y′′ + xy′ + (x^{2} − n^{2})y = 0 (Bessel’s equation.)

Ans: .

b) (1 − x^{2})y′′ − 2xy′ + n(n + 1)y = 0 (Legendre’s Equation.)

Ans: .

Name:

6. Find the general solution of y′′ − 2y′ + 10y = 0

Ans: .

7. Solve the equation: y′′ − 2y′ − 3y = 4e^{2t}

Ans: .

8. Given that y_{1} = t is a solution t^{2}y′′ + 2ty′ − 2y = 0, find another l.i. solution

Ans: .

9. Write a suitable undetermined coefficient form for the particular solution of:

a) y′′ + 16y = x cos 4x + 5x^{2}

a) .

b) y′′ − 5y′ + 6y = e^{t} cos 2t + 3t^{2}e^{2t}

b) .

10. Solve by variation of parameters (See Pb. 7): y′′ − 2y′ − 3y = 4e^{2t}

Ans: .