Solve the initial value problem.

x squared StartFraction dy Over dx EndFractionequalsStartFraction $2$ x squared minus x minus $5$ Over left parenthesis x plus $1$ right parenthesis left parenthesis y plus $1$ right parenthesis EndFraction$,$

y left parenthesis $1$ right parenthesis equals $4$

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Part $1$

Begin by separating the variables. Choose the correct answer below.

A$.$left parenthesis y plus $1$ right parenthesis dy equals StartFraction $2$ x squared minus x minus $5$ Over x squared left parenthesis x plus $1$ right parenthesis EndFraction dx

left parenthesis y plus $1$ right parenthesis dy equals StartFraction $2$ x squared minus x minus $5$ Over x squared left parenthesis x plus $1$ right parenthesis EndFraction dx

Your answer is correct.

B$.$StartFraction x squared left parenthesis x plus $1$ right parenthesis Over $2$ x squared minus x minus $5$ EndFraction dy equals StartFraction $1$ Over y plus $1$ EndFraction dx

StartFraction x squared left parenthesis x plus $1$ right parenthesis Over $2$ x squared minus x minus $5$ EndFraction dy equals StartFraction $1$ Over y plus $1$ EndFraction dx

C$.$StartFraction dy Over dx EndFraction equals StartFraction $2$ x squared minus x minus $5$ Over x squared left parenthesis x plus $1$ right parenthesis left parenthesis y plus $1$ right parenthesis EndFraction

StartFraction dy Over dx EndFraction equals StartFraction $2$ x squared minus x minus $5$ Over x squared left parenthesis x plus $1$ right parenthesis left parenthesis y plus $1$ right parenthesis EndFraction

D$.$

The equation is already separated.

Part $2$

The solution is

enter your response here.

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