Integration(differential equations and first order homogenous differentail equations)

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.

Re: Integration(differential equations and first order homogenous differentail equati

Alexander

I have noticed that most of them are simple D.E with separable variables.

first step separate the variables left the y right the x

then integrate it is not difficult

example get the second one dy/dx =6/(x^2-9)

after you separate the variables you must get dy=(6/x^2-9)dx

and after integration you will get y= ln|x-3|-ln|x+3| +C ,where c is the constant of integration...

good luck with the remaining.

MINOAS

Minoas

Re: Integration(differential equations and first order homogenous differentail equati