Consider the differential equation: $y^{\text{'}\text{'}}-7y-30y=0$

a$.[5$ pts$]$ Verify that, for any constants A and $B,$ the following family of functions are solutions to the above differential equation:

$y=A{e}^{-3x}B{e}^{10x}$

b$.[5$ pts$]$ Find the values A and $B$ that make the above general solution into a solution for the following initial value problem:

$y^{\text{'}}-7y^{\text{'}}-30y=0$;$y(0)=4,y(0)=1$

$($Note: I am expecting you to use only the knowledge from MATHConsider the differential equation: $y^{\text{'}\text{'}}-7y-30y=0$

a$.[5$ pts$]$ Verify that, for any constants A and $B,$ the following family of functions are solutions to the above differential equation:

$y=A{e}^{-3x}B{e}^{10x}$

b$.[5$ pts$]$ Find the values A and $B$ that make the above general solution into a solution for the following initial value problem:

$y^{\text{'}}-7y^{\text{'}}-30y=0$;$y(0)=4,y(0)=1$

$($Note: I am expecting you to use only the knowledge from MATH