Okay, that makes sense.
Going back to before dividing by x:
u + x du/dx = [ 1 + u2 ] / 5u
Subtract the u:
x du/dx = [ 1 - 4u2 ] / 5u
Rearrange to get du and dx on each side:
[ 1/x ] dx = [ 5u / [ 1 - 4u2 ] ] du
Then integrating:
ln( x ) + C = [ -5/8 ] ln( 1-4u2 )
Raise e to all terms...
Homework Statement
Find an equation that defines IMPLICITLY the parameterized family of solutions y(x) of the differential equation:
5xy dy/dx = x2 + y2
Homework Equations
y=ux
dy/dx = u+xdu/dx
C as a constant of integration
The Attempt at a Solution
I saw a similar D.E. solved using the y=ux...
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