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

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

The differential equation which represents the family of curves

The differential equation which represents the family of curves y = c₁e^c₂x where c₁ and c₂ are arbitrary constants, is

yy'' = y'
y'' = y'y
y' = y²
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

0
2e
e
2

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

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

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

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