Consider the differential equation y prime(t)minus2y(t)equals10, y(0)equals4. a. Find a power series for the solution of the differential equation. b. Identify the function represented by the power series. a. Choose the correct answer below. A. y(t)equals4 plus 18 t plus 18 t squared plus 12 t cubed plus font size decreased by 4 times times times plus StartFraction 18 times 2 Superscript n minus 1 Over n exclamation mark EndFraction t Superscript n Baseline plus font size decreased by 4 times times times B. y(t)equals10 minus 18 t plus 18 t squared minus 12 t cubed plus font size decreased by 4 times times times plus StartFraction (negative 1 )Superscript n Baseline 18 times 2 Superscript n minus 1 Over n exclamation mark EndFraction t Superscript n Baseline plus font size decreased by 4 times times times C. y(t)equals4 minus 18 t plus 18 t squared minus 12 t cubed plus font size decreased by 4 times times times plus StartFraction (negative 1 )Superscript n Baseline 18 times 2 Superscript n minus 1 Over n exclamation mark EndFraction t Superscript n Baseline plus font size decreased by 4 times times times D. y(t)equals10 plus 18 t plus 18 t squared plus 12 t cubed plus font size decreased by 4 times times times plus StartFraction 18 times 2 Superscript n minus 1 Over n exclamation mark EndFraction t Superscript n Baseline plus font size decreased by 4 times times times b. y(t)equals nothing