Find the particular solution of the differential equation dydx + 2ytanx = sinx, given that y = 0 when x = π/3.

Given the equation is dydx + 2ytanx = sinx
Multiplying by sec²(x) on both sides
dydxsec²(x) + 2ysec²(x)tanx = sinxsec²(x)
This can be written as d(ysec²(x))/dx = tan(x)sec(x)
Thus, integrating on both the sides, we get,
⇒ ysec²(x) = sec(x) + c is the general solution
On substituting the values, y = 0 when x = π/3 we get c = -2
Thus the particular solution on substituting the values is ysec²(x) = sec(x) - 2