Find the function [tex] y_{1} (t)[/tex] which is the solution of [tex]64y'' +48y' +8y=0[/tex] with initial conditions. [tex] y_{1} (0)=1, y_{1}' (0)=0[/tex]
Find the function [tex] y_{2} (t)[/tex] which is the solution of [tex]64y'' +48y' +8y=0[/tex] with initial conditions. [tex] y_{2} (0)=0, y_{2}' (0)=1[/tex]
Find the Wronskian [tex]W(t)=W(y_{1},y_{2})[/tex]
Remark: You can find W by direct computation and use Abel's theorem as a check. You should find that W is not zero and so [tex] y_{1}[/tex] and [tex] y_{2}[/tex]form a fundamental set of solutions of the above equation.