Final answer:
The integrating factor for the given differential equation is xe^(xy^2).
Step-by-step explanation:
An integrating factor for the differential equation dy + y/dx = e^(3x)dx is xe^(xy^2).
To find the integrating factor, we need to rewrite the equation in the form M(x,y)dx + N(x,y)dy = 0, where M(x,y) = 1 and N(x,y) = y.
Multiplying the entire equation by the integrating factor, we obtain xye^(xy^2)dx + x^2ye^(xy^2)dy = xe^(3x)dx.