Answer:
Step-by-step explanation:
First step: I'm going to solve our substitution for y:
Multiply both sides by x:
Second step: Differentiate the substitution:
Third step: Plug in first and second step into the given equation dy/dx=f(x,y):
We are going to simplify what we can.
Every term in the fraction on the right hand side of equation contains a factor of so I'm going to divide top and bottom by
:
Now I have no idea what your left hand side is suppose to look like but I'm going to keep going here:
Subtract u on both sides:
Find a common denominator: Multiply second term on right hand side by :
Combine fractions while also distributing u to terms in ( ):
Third step: I'm going to separate the variables:
Multiply both sides by the reciprocal of the right hand side fraction.
Divide both sides by x:
Reorder the top a little of left hand side using the commutative property for addition:
The expression on left hand side almost matches your expression but not quite so something seems a little off.