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Mathematics
Mathematics
Problem
Verify that the function
y
=
c
1
e
a
x
cos
b
x
+
c
2
e
a
x
sin
b
x
y = c_1 e^{ax} \cos bx + c_2 e^{ax} \sin bx
y
=
c
1
e
a
x
cos
b
x
+
c
2
e
a
x
sin
b
x
, where
c
1
,
c
2
c_1, c_2
c
1
,
c
2
are constants, is a solution of the differential equation
d
2
y
d
x
2
−
2
a
d
y
d
x
+
(
a
2
+
b
2
)
y
=
0
\frac{d^2 y}{dx^2} - 2a \frac{dy}{dx} + (a^2 + b^2) y = 0
d
x
2
d
2
y
−
2
a
d
x
d
y
+
(
a
2
+
b
2
)
y
=
0
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