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Mathematics
Problem
Determine whether the function
y
(
x
)
=
x
e
2
x
y(x)=x e^{2x}
y
(
x
)
=
x
e
2
x
satisfies the differential equation
y
′
′
−
4
y
′
+
4
y
=
0
y''-4y'+4y=0
y
′′
−
4
y
′
+
4
y
=
0
. Write the simplified form of
y
′
′
−
4
y
′
+
4
y
y''-4y'+4y
y
′′
−
4
y
′
+
4
y
and state your conclusion.
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