Question

Find the general solution to y′′−4y′+8y=0

Answer 1

Answer:

Independent Solutions:

By writing the characteristic polynomial, we can solve the homogenous linear differential equations.

For the particular case in which the roots are complex, two independent solutions of the form can be obtained:

r

1

=

α

+

β

i

,

r

2

=

α

−

β

i

→

y

1

=

e

α

x

cos

(

β

x

)

,

y

2

=

e

α

x

sin

(

β

x

)

Answer and Explanation:

Writing the characteristic polynomial, we have:

{eq}y'' - 4y' + 8y = 0\\ {r^2} - 4r + 8 = 0\\ r = \frac{{4 \pm \sqrt {{{\left( { - 4} \right)}^2} -...

See full answer below.

Answer 2

Step-by-step explanation:

2y"-4y'+8y=0 find the general solution of the equation