Consider the Initial Value Problem

What Is the Solution $y=\left(\frac{\alpha}{2}-\frac{8}{7}\right) e^{\frac{7}{4} t}+\left(\frac{\alpha}{2}+\frac{8}{7}\right) e^{\frac{7}{4} t}$

Multiple Choice

Consider the initial value problem

What is the solution of this initial value problem?

A) $y=\left(\frac{\alpha}{2}-\frac{8}{7}\right) e^{\frac{7}{4} t}+\left(\frac{\alpha}{2}+\frac{8}{7}\right) e^{\frac{7}{4} t}$
B) $y=\left(\frac{\alpha}{2}+\frac{8}{7}\right) e^{\frac{7}{4} t}+\left(\frac{\alpha}{2}-\frac{8}{7}\right) e^{\frac{7}{4} t}$
C) $y=\left(\frac{\alpha}{2}+\frac{8}{7}\right) e^{\frac{4}{7} t}+\left(\frac{\alpha}{2}-\frac{8}{7}\right) e^{\frac{4}{7} t}$
D) $y=\left(\frac{a}{2}-\frac{8}{7}\right) e^{\frac{4}{7} t}+\left(\frac{a}{2}+\frac{8}{7}\right) e^{\frac{4}{7} t}$