Find the general solution to the homogeneous differential equation:
(d2y/dt2)+10(dy/dt)+24y=0

the solution can be written in the form:

y=c1er1t+c2er2t

with r1
using this form, r1= ? and r2 = ?

Step-by-step explanation:

and are the eingenvalues of the equation, that is

the values of r when

Using r = (dy/dt).

They are

r2 is larger than r1, so

That's a right triangle

remember, if  the legs of a right triangle measure a and b and the hypootnuse is c then a²+b²=c²

so

hypotnuse is longest side, the one oposite the right angle
in this case, it is 5
one leg is 4
and the other one is red, let's call it x

so
x²+4²=5²
x²+16=25
minus 16 both sides
x²=9
sqrt both sides
x=3

the length of the red vertical edge is 3cm