# Differential Equation

### 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. 1/3
2. -2/3
3. -1/3
4. 4/3

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

The differential equation which represents the family of curves y = c1ec2x where c1 and c2 are arbitrary constants, is

1. yy'' = y'
2. y'' = y'y
3. y' = y2
4. yy'' = (y')2

### 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

1. 0
2. 2e
3. e
4. 2

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

The solution of the equation d2y/dx2 = e-2x is

1. e-2x/4
2. 1/4 * e-2x + cx2 + d
3. e-2x/4 + cx + d
4. 1/4 * e-4x + cx + d

### 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 = 4d3y/dx3 are

1. (3, 3)
2. (3, 1)
3. (1, 2)
4. (1, 2/3)