Question $4$

$10$ pts

$4.y_1(x)=x$ is a solution to the equation

$x^2{y}^{\text{'}\text{'}}-x{y}^{\text{'}}+y=0$

Let $y_2$ be a second, independent solution of the equation, and let $y(x)=c_1{y}_1(x)+c_2{y}_2(x)$ be the solution to the initial value problem:

$x^2{y}^{\text{'}\text{'}}-x{y}^{\text{'}}+y=0,y(2)=2,y^{\text{'}}(2)=3$

Then $y(1)=$

Then $y(1)=?$

$1\mathrm{.}6137,$

$-0\mathrm{.}77258$

$1$

None of the other answers,

$0\mathrm{.}38629$