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 P: 1,035 For example: $$\frac{dy}{dx} + y = e^{3x}$$ I understand that these differential equations are most easily solved by multiplying in a factor of integration, and then comparing the equation to the product rule to solve et al.. For example: $$t\frac{dy}{dx} + 2t^{2}y = t^{2}$$ $$\frac{dy}{dx} + 2ty = t$$ Multiplying in an integration factor u(x), which in this case: $$u(x) = e^{\int{2t}dt} = e^{t^{2}}$$ $$e^{t^{2}}\frac{dy}{dx} + 2te^{t^{2}}y = te^{t^{2}}$$ Now I can compress the left side down using the product rule and all that. I don't understand how they are getting u(x) or why it's equal to e^{\int{2t}dt} ?