guys need help on ODE questions,

i just need you guys to tell me what method to use for the following equations and i will try solve them myself:

a) (2y+tany)dx +(x-x^2(tany))dy=0
b) y'=(e^x)(2y+(e^x))+y(1+y)
c) y'=1+y^2-x^2

any hints will be good also. XD

And i am solving to get its general solution, so just tell me what method to use as in like homogenous, exact, integrating factor, bernouli, etc...

Thanks

google is your friend:

(a) https://answers.yahoo.com/question/index?qid=20131112055820AAxrUAf

(b),(c) Check out Riccati equations

y' = y^2 + q(x)y + p(x)

Sure! I can help you with those ODE questions. Here are some hints to determine the method you can use to solve each equation:

a) (2y + tan(y))dx + (x - x^2tan(y))dy = 0

This is a first-order linear ODE. To solve it, you can use the method of integrating factors. Look for an integrating factor that can make the equation exact:

Multiply the entire equation by a suitable integrating factor μ(x,y):
μ(x,y) [(2y + tan(y))dx + (x - x^2tan(y))dy] = 0

Then, you can use the fact that the equation μ(x,y) M(x,y)dx + μ(x,y)N(x,y)dy = 0 is exact if M_y = N_x to determine μ(x,y). Once you find μ(x,y), you can solve the equation by integrating both sides.

b) y' = e^x(2y + e^x) + y(1 + y)

This is a first-order nonlinear ODE. To solve it, you can use the method of separation of variables. Rearrange the equation to have all the terms with y on one side and all the terms with x on the other side:

dy/dx - (e^x)(2y + e^x) - y(1 + y) = 0

You can then separate the variables by dividing both sides by the terms involving y and multiplying both sides by dx:

(1/(2y + e^x + y(1 + y)))dy = (e^x)dx

Now, you can integrate both sides to find the solution.

c) y' = 1 + y^2 - x^2

This is a first-order nonlinear ODE. To solve it, you can use the method of separable variables. Rearrange the equation to have all the terms with y on one side and all the terms with x on the other side:

dy/dx - (1 + y^2) + x^2 = 0

You can then separate the variables by dividing both sides by the terms involving y and multiplying both sides by dx:

(1/(1 + y^2 - x^2))dy = dx

Now, you can integrate both sides to find the solution.

Remember, these hints provide the methods you can use to solve the given ODEs. To actually solve the equations, you need to follow the specific steps of each method.