In 1–14, find a general solution for the differential equation with x as the independent variable.

Solution :Step 1 of 3 : In this problem, we need to find a general solution for the differential equation with x as the independent variable.y’’’ + 2 y’’ - 8 y = 0Step 2 of 3 : The auxiliary equation is m³ + 2 m² - 8 m = 0 Factor this equation m (m² + 2 m - 8) = 0m (m-2) (m+4) = 0 The roots of the auxiliary equation is 0, 2 and -4.