iven the second$-$order, linear, homogeneous differential equation

$y-10y+25y=0$

and the functions

$y1(x)=e5x$

$y2(x)=xe5x$

$(a)$ Verify that $y1(x)$ and $y2(x)$ are solutions $to$ the given differential equation.

$(b)$ Verify that $y1(x)$ and $y2(x)$ are linearly independent using the Wronskian.

$(c)y1(x)$ and $y2(x)$ form a fundamental set $of$ solutions $to$ the linear, homogeneous differential equation. Find the

general solution.

$(d)$ Let $y(0)=1$ and $y(0)=2.$ Find the solution $to$ the initial$-$value problem.