Question 1204822
y= A/x + Bx where A and B are constants, show that x²dy/dx +xdy/dx=y
<pre>
I don't believe that's true. Let's see if we can find a counter-example.

{{{y=A/x+Bx}}}
{{{y=Ax^(-1)+Bx}}}
{{{dy/dx=-Ax^(-2)+B}}}

Now if {{{x^2*expr(dy/dx) +x*expr(dy/dx)=y}}} were true it would be true when A=B=x=1 

{{{y=A/x+Bx=1/1+1(1)=1+1=2}}}

{{{dy/dx=-Ax^(-2)+B=-(1)(1)^(-2)+1=-1+1=0}}}

So we substitute in

{{{x^2*expr(dy/dx) +x*expr(dy/dx)=y}}}

{{{(1)^2*0+1*0=2}}}

{{{0=2}}}

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

Edwin</pre>