1.

Classify

the

following

equation(s)

(Linear

or

Nonlinear

and

its

order).

Note

that y(x)

a

y"-2x%y

-5y

=2¢*

b

*y®

-

3y"

=

4y

sin(x)

o

}"731}“{'7)(:21*5

d.

¥

(22

-

4x

+2y') =

tan(x)

+

2y’

2.

Provethat

y(x)

=

2¢*

—

xe*

is

a

solution

to

the

equation

y"

+y

=

2y

3.

Given

that

y(x)

=

C;5in(2x)

+

C;c05(2x)

is a

general

solution

to

"

+

4y

=

0.

Find

the

solution

to

the

given

initial

condition

y(0)

=

4

and

y(m/3)

=

1

4.

Given

f(x)

=

€%,

g(x)

=

cos(x),

and

h(x)

=

sin(x),

are

they

lincarly

independent?

Why?