Use the method for solving homogeneous equations to solve the following differential equation.

left parenthesis $5$ x squared minus y squared right parenthesis dx plus left parenthesis xy minus $2$ x cubed y Superscript negative $1$ Baseline right parenthesis dy equals $0$

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Part $1$

Ignoring lost$$ solutions, if$$ any, an implicit solution in the form

$$F$($x$,$y$)$equalsC

is

enter your response hereequals$$C$,$

where C is an arbitrary constant.

$($Type an expression using x and y as the variables. Use parentheses to clearly denote the argument of each$$ function.$)$