Consider the following differential equations.

$y\frac{dx}{dy}-x=3y^2,x(6)=1$

Find the coefficient function $P(y)$ when the given differential equation is written in the standard form $\frac{dx}{dy}+P(y)x=f(y).$

$P(y)=$

$$

Find the integrating factor for the differential equation.

$e^{{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}P(y)dy}=$

$$

Solve the given initial$-$value problem.

$x(y)=$

$$

Give the largest interval I over which the solution is defined. $($Enter your answer using interval notation.$)$

$I=$