Show that

a) Y= x exp-x statisfies the equation xy'=(1-x)y

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- February 10th 2009, 09:38 PMhomerbDerivatives Of inverse functions; Derivatives and integrals involving exponential fun
Show that

a) Y= x exp-x statisfies the equation xy'=(1-x)y - February 10th 2009, 09:42 PMo_O
Use product rule to get:

So:

And:

Are they equal? If so, you're done. - February 10th 2009, 09:50 PMhomerb
do I have to use ln?

or what is the next step - February 10th 2009, 09:53 PMo_O
What do you mean? We just want to show .

We've got an expression for and one for . Show that they're equal by simplifying and you're done. - February 10th 2009, 09:54 PMhomerb
oh I see thanks, I thinking something else?