Question

Kindly Clarify this... when i try to find the solution of a first order autonomous differential equation by using the integrating factor method used for linear first order DEs i m getting only a constant solution. What about the other general solutions??

Answer 1

An example of a forst order autonomous d.e. is:

y'= 2y+3, or \(\frac{dy}{dx}=2y+3\), so assuming y is a function of x.

The integrating factor is \(e^{\int2dx}=e^{2x}\).
General solution:

\(y=e^{2x}(\int e^{-2x}\cdot3dx+C)\), where C is a real constant.

This can be simplified to:

\(y=e^{2x}(-\frac{3}{2}e^{-2x}+C)=-\frac{3}{2}+Ce^{2x}\).

The constant solution occurs for C=0.

Answer 2

holy sh*t, this is a year old

Answer 3

Thanks anyway :)

Answer 4

Thank you ZeHanz....

Answer 5

yw!

Answer 6

Hope my answer wasn't too late :)

Answer 7

Late is always better than never...:-)