Answer:
Step-by-step explanation:
To find the solution of a given differential equation ay''+by'+cy=0, a≠0, you have to consider the quadratic polynomial ax²+bx+c=0, called the characteristic polynomial.
Using the quadratic formula, this polynomial will always have one or two roots, for example r and s. The general solution of the differential equation is:
, if the roots r and s are real numbers and r≠s.
, if r=s is real.
, if the roots r and s are complex numbers α+βi and α−βi
.
In this case, the characteristic polynomial is:
Since the roots are complex numbers, with α=0 and β=1, then the answer is: