Apply the standard $RK4$ method $to$ the following initial value problem:

$t^2\frac{d^{2}y}{d{t}^2}-2t\frac{dy}{dt}+2y=t^{3}lnt$

$y(1)=-1$

$y^{\text{'}}(1)=0$

with a step size $ofh=0\mathrm{.}25in$ the interval $1,3\mathrm{.}5$

Start $by$ transforming this second order differential equation into a system $of$ first order

differential equations $by$ using the variables

$y_1=y$

$y_2=\frac{dy}{dt}$

Give the approximations $w_1$ and $w_{2}of{y}_1$ and $y_{2}int=3\mathrm{.}5.$

Use $16$ digits $in$ your calculations and give the answers with $at$ least $5$ significant digits

$w_1(t=3\mathrm{.}5)=$

$w_2(t=3\mathrm{.}5)=$