Question

Find the general solution of the given second-order differential equation. y'' − y' − 20y = 0

Answer 1

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Y= 0, 21

Answer 2

Taking common factors

y (y'-y-20)=0


there are two possible solutions

y=0

or

y'-y-20y=0

thus using the formula
$( - b + or - \sqrt{ {b}^{2} - 4ac} ) \div 2a$
where a is 1 b is -1 and c is -20

but as you substitute the answer inside the root is negative and that cant be possible so the question has no zero and the only possible solution is

y=0