lower order differential equation

Question

how to solve the differention equation 4d⁴-8d³-7d²+11d+6

please tell me that how i will obtain the complete solution ofthis differention equation

Answer 1

The roots of the primitive equation. 4D ⁴ -8D ³ -7D ² + 11D + 6 + 0. Are. -1, -1/2, 3/2, and 2

So, try the general solution. Y = Ae ^-1 + Be ^-.5 + Ce ^1.5 + De ² + E

where A,B,C,D,E are constants