it is a first-order linear DE
I have begun studying differential equations and I think I understand problems involving two variables of x and y, but the first problems they have listed involve e
dy/dx = e^x+y
Ok, I would think that you would do something like this:
dy/dx -e^x = dy/dx e^y
but really am unsure...
Please advise.
This is an inhomogeneous linear 1-st order ODE. Its general solution is
the sum of the general solution to the homogeneous equation:
and a particular integral of:
We solve the homogeneous equation by using a trial solution , which when substituted into the equation gives us the
indicial equation:
So the general solution of the homogeneous equation is .
Now as the right hand side of the inhomogeneous equation is in fact a solution of the homogeneous equation tradition dictates that we try out as a particular solution. In this case:
so is indeed a particular integral as expected, so the general solution to the original ODE is:
RonL