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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 = ?

Respuesta :

Answer:

[tex]r_{1} = -6, r_{2} = -4[/tex]

Step-by-step explanation:

[tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the eingenvalues of the equation, that is

the values of r when

[tex]r^{2} + 10r + 24 = 0[/tex]

Using r = (dy/dt).

They are

[tex]r = -6, r = -4[/tex]

r2 is larger than r1, so

[tex]r_{1} = -6, r_{2} = -4[/tex]

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