Consider the differential equation

$(x-1)y^{\text{'}\text{'}}-2x{y}^{\text{'}}+(x+1)y=0,x>1$

The function $y_1(x)=e^x$ is one of solutions.

Choose the function $y_2$ such that $y_1$ and $y_2$ form fundamental set of solutions.

$y_2(x)=(x-1{)}^3{e}^x$

$y_2(x)=(x-1{)}^2{e}^x$

$y_2(x)=x-1$

$y_2(x)=(x-1{)}^2$Consider the differential equation

$(x-1)y^{\text{'}\text{'}}-2x{y}^{\text{'}}+(x+1)y=0,x>1$

The function $y_1(x)=e^x$ is one of solutions.

Choose the function $y_2$ such that $y_1$ and $y_2$ form fundamental set of solutions.

$y_2(x)=(x-1{)}^3{e}^x$

$y_2(x)=(x-1{)}^2{e}^x$

$y_2(x)=x-1$

$y_2(x)=(x-1{)}^2$Consider the differential equation

$(x-1)y^{\text{'}\text{'}}-2x{y}^{\text{'}}+(x+1)y=0,x>1$

The function $y_1(x)=e^x$ is one of solutions.

Choose the function $y_2$ such that $y_1$ and $y_2$ form fundamental set of solutions.

$y_2(x)=(x-1{)}^3{e}^x$

$y_2(x)=(x-1{)}^2{e}^x$

$y_2(x)=x-1$

$y_2(x)=(x-1{)}^2$