SOLUTION: If y= A/x + Bx where A and B are constants, show that x²dy/dx +xdy/dx=y

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Question 1204822: If
y= A/x + Bx where A and B are constants, show that x²dy/dx +xdy/dx=y
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
y= A/x + Bx where A and B are constants, show that x²dy/dx +xdy/dx=y
I don't believe that's true. Let's see if we can find a counter-example.

y=A%2Fx%2BBx
y=Ax%5E%28-1%29%2BBx
dy%2Fdx=-Ax%5E%28-2%29%2BB

Now if x%5E2%2Aexpr%28dy%2Fdx%29+%2Bx%2Aexpr%28dy%2Fdx%29=y were true it would be true when A=B=x=1 

y=A%2Fx%2BBx=1%2F1%2B1%281%29=1%2B1=2

dy%2Fdx=-Ax%5E%28-2%29%2BB=-%281%29%281%29%5E%28-2%29%2B1=-1%2B1=0

So we substitute in

x%5E2%2Aexpr%28dy%2Fdx%29+%2Bx%2Aexpr%28dy%2Fdx%29=y

%281%29%5E2%2A0%2B1%2A0=2

0=2

False. That's why I don't believe what you are asking to prove is true.

Edwin
 

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

Wrong statement.