The trouble is this is not a separable equation.
You have to use an integrating factor .
Do you know this method ?
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