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?
