One of the following is a general solution of the homogeneous differential equation $3x^{2}y''+7xy'+y=0$
$$\begin{aligned} y&=\frac{a}{x^2}+ \frac{b}{x^{\frac{1}{9}}} \\ y&=\frac{a}{x}+\frac{b}{x^{\left({\frac{1}{3}}\right)}} \\ \end{aligned}$$ and one of the following is a solution to the nonhomogeneous equation $3x^{2}y''+7xy'+y=16x+6$ $$\begin{aligned} y&=x^2-x \\ y&=6+2x \\ y&=e^x \\ \end{aligned}$$ By superposition, the general solution of the equation $3x^{2}y''+7xy'+y=16x+6$ is
$y =$
Find the solution with
$$\begin{aligned} y(1)&=8 \\ y^\prime(1)&=9 \\ \end{aligned}$$ $y =$

Fortunately, since I already had it computed, my professor also asked me to find the Wronskian (using only the solutions to the homogeneous equation, without the coefficients a and b) . The fundamental theorem shows that this solution is the unique solution to the IVP on the interval