Here's my unsolved questions, alas, there was many questions that I can't managed to solve it. Please show me the steps and don't just give me the answer. Thanks in advance.
Expressing y in terms of x.
(1) (y/ sec^2 x)dy/dx = 2tan x + 1
(2) dy/dx = 6/(x^2 -9)
(3) (sin^2 x)dy/dx = (cos x)/y
(4) (1 - x^2)dy/dx = y(1+x^2)
(5) (y)dy/dx = √(1-y^2)
(6) (1/x)dy/dx = y^2 sec^2 x
(7) By substitution y = vx , show that x(x+y)dy/dx = x^2 + y^2 is y + x ln ((x-y)^2 /x) = 0 when y = 0 and x = 1.
(8) By substitution u = 4x + y, find the particular solution of the differential equation dy/dx = 4x + y when y = 1 and x = 0.
(9) By substitution z = 2x - 3y, show that (2x - 3y + 3)dy/dx = 2x - 3y + 1 is 2ln ( 3 - 2x + 3y ) = 1 - x + y when y = 0 and x = 1.
Please take your time, I'm having hard time solving these problems, again, thank you very much.