Find a family of solutions to the DE dy/dx+ 2xy=1
I have some trouble separating the variables...anyone can give me a general method on how to do that?
oh sorry let me rephrase the question:
Verify that the indicated family of functions is a solution to the DE dy/dx+2xy=1:
y= (e^-x^2)*integral from x to 0 (e^(t^2)dt)+ce^(-x^2)
where c is an arbitrary constant.
I suppose the e^t^2 is the integrating factor??
I tried to substitute the y equation into the DE but it does not work.
If You write the DE as...
(1)
... it is easy to see that it's a linear DE on the form...
(2)
... where and and its solution can be found is 'standard fashion' ...
(3)
The integral in (3) is not elementary but it can be expressed as a convergent series...
Kind regards