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## Main Question or Discussion Point

im in calculus 2 right now and we are doing differential equaitons right now. im confused as to why when i find the integrating factor I(x)=e^(∫p(x) and when i multiply both sides i get

e^∫(p(x))[(dy/dx)+p(x)*y]=d(e^(p(x)dx)*y) how are they equal. i will give an example.

(dy/dx)+y=x*e^(x) the integrating factor is e^(∫dx)=e^(x) then i multiply both sides by

e^(x) which gives

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

which is equal to:

d[e^(x)*y]/dx=e^(x)*x; basically my question is how do you get here? how does e^(x)*dy/dx just disappear after i multiply the integrating factor to both sides?

please help with what happens after this step: e^(x)*[(dy/dx)+y]=e^(x)*[x*e^(x)]

e^∫(p(x))[(dy/dx)+p(x)*y]=d(e^(p(x)dx)*y) how are they equal. i will give an example.

(dy/dx)+y=x*e^(x) the integrating factor is e^(∫dx)=e^(x) then i multiply both sides by

e^(x) which gives

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

which is equal to:

d[e^(x)*y]/dx=e^(x)*x; basically my question is how do you get here? how does e^(x)*dy/dx just disappear after i multiply the integrating factor to both sides?

please help with what happens after this step: e^(x)*[(dy/dx)+y]=e^(x)*[x*e^(x)]