$(2-4)$ Solve the following first order differential equations with any method you like.

$y^{\text{'}}+\frac{2}{t}y=t-1+\frac{1}{t}$;$y(1)=\frac{1}{2}$

$y^{\text{'}}=\frac{x{y}^3}{\sqrt[\phantom{2}]{1+x^2}}$

$xy{y}^{\text{'}}+4x^2+y^2=0$

Verify $y^{3}dx+3x{y}^{2}dy=0$ is an exact equation, then find the solution.

Solve the following higher order equations with any method you like.

$6.y^{\text{'}\text{'}}-3y^{\text{'}}+2y=0$