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## Main Question or Discussion Point

Hi everyone, any help with this would be greatly appreciated..

I have been practicing simple differential equations for a couple months now and kinda just taking it easy and enjoying building my intuition. i have encountered a chapter in my text by Backhouse (pure mathematics 2) involving first order exact equations as a prelude to using integrating factors. It shows by example an inseparable differential equation..

2xy [dy/dx] +y^2 = e^(2x)

whose LHS is said to be equal to the derivative of the product (xy^2). The trouble i'm having here is that when i check and differentiate (xy^2) by product rule, i wind up with just 2xy + y^2. My question is where does the factor of [dy/dx] in the original equation come from? i suspect that i might be doing something wrong here?

I have been practicing simple differential equations for a couple months now and kinda just taking it easy and enjoying building my intuition. i have encountered a chapter in my text by Backhouse (pure mathematics 2) involving first order exact equations as a prelude to using integrating factors. It shows by example an inseparable differential equation..

2xy [dy/dx] +y^2 = e^(2x)

whose LHS is said to be equal to the derivative of the product (xy^2). The trouble i'm having here is that when i check and differentiate (xy^2) by product rule, i wind up with just 2xy + y^2. My question is where does the factor of [dy/dx] in the original equation come from? i suspect that i might be doing something wrong here?