1
###
If (2 + sin x) dy/dx + (y + 1)cos x = 0 and y(0) = 1

If (2 + sin x) dy/dx + (y + 1)cos x = 0 and y(0) = 1, then y(π/2) is equal to

- 1/3
- -2/3
- -1/3
- 4/3

2
###
The differential equation which represents the family of curves

The differential equation which represents the family of curves y = c_{1}e^{c2x} where c_{1} and c_{2} are arbitrary constants, is

- yy'' = y'
- y'' = y'y
- y' = y
^{2} - yy'' = (y')
^{2}

3
###
Let y(x) be the solution of the differential equation

Let y(x) be the solution of the differential equation (x log x)(dy/dx) + y = 2x log(x), (x≥1). Then y(e) is equal to

- 0
- 2e
- e
- 2

4
###
The solution of the equation d^2y/dx^2 = e^-2x is

The solution of the equation d^{2}y/dx^{2} = e^{-2x} is

- e
^{-2x}/4 - 1/4 * e
^{-2x}+ cx^{2}+ d - e
^{-2x}/4 + cx + d - 1/4 * e
^{-4x}+ cx + d

5
###
The order and degree of the differential equation (1 + 3dy/dx)^2/3 = 4d^3y/dx^3 are

The order and degree of the differential equation (1 + 3dy/dx)^{2/3} = 4d^{3}y/dx^{3} are

- (3, 3)
- (3, 1)
- (1, 2)
- (1, 2/3)