Differential Equation
1. Determine the order and degree of the differential equation….
A. Fourth order, first degree
B. Third order, first degree
C. First order, fourth degree
D. First order, third degree
2. Which of the following equations is a variable separable DE?
A. (x + x2y)dy + (2x + xy2)dx
B. (x + y)dx – 2y dy = 0
C. 2y dx = (x2 +1)dy
D. y2 dx + (2x – 3y)dy = 0
3. Obtain the particular solution of dr/dt = -4rt when t = 0, r = ro
A. r = 2ro e-2t^
2
C. r = ro e2t^
2
B. r = 2ro e-t^
2
D. r = ro e-2t^
2
4. Which of the following equations is an exact DE?
A. (X2 + 1)dx – xy dy = 0
B. x dy + (3x – 2y) dx = 0
C. 2xy dx + (2 + x2)dy = 0
D. x2y dy – y dx = 0
5. Solve the equation (6x + y2)dx + y(2x – 3y)dy = 0
A. xy2 + 3x2 – y3 = c
B. 3xy2 – 3x2 – y3 = c
C. xy2 + 2x2 – 3y3 = c
D. xy2 + 3x2 – y2 = c
6. Obtain the particular solution of (3x2 – 2y2)y’ = 2xy; when x = 0, y = -1
A. x2 = 2y2(y + 1) C. x2 = 2y2(y -1)
B. x2 = y2(y + 1) D. x2 = y2(y - 1)
7. Solve the equation dy/dx + 2/x y = 6x3
A. xy2 = 6x5 + c C. x2y2 = 6x5 + c
B. x2 = 5x6 + c D. x2y = x6 + c
8. Find the general solution of d2s/dt2 + 2 ds/dt + 5s = 0
A. s = e-t(C1cos2t + C2sin2t) C. s = e-2t(C1cos2t + C2sin2t)
B. s = 2e-t(C1cos2t + C2sin2t) D. s = 2e-2t(C1cos2t + C2sin2t)
9. Radium decomposes at a rate proportional to the amount at any instant. In
100 years, 100mg of radium decomposes to 96mg. How many mg will be left
after 100 years?
A. 88.60 C. 92.16
B. 95.32 D. 90.72
