Substitute $y(x)={\displaystyle \underset{n=0}{\overset{}{}}}{a}_n{x}^n$ and the Maclaurin series for $5sinx$ into $y^{\text{'}}-6xy=5sinx$ and equate the coefficients of like powers of $x$ on both sides of the equation to find the first four nonzero terms in a power series expansion about $x=0$ of general solution to the differential equation.

$y(x)=$

$+$cdots

$($Type an expression in terms of $a_0$ that includes all terms up to order $6.)$