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Mathematics
Mathematics
Problem
14. If
y
=
A
e
m
x
+
B
e
n
x
y=\mathrm{A} e^{m x}+\mathrm{B} e^{n x}
y
=
A
e
m
x
+
B
e
n
x
, show that
d
2
y
d
x
2
−
(
m
+
n
)
d
y
d
x
+
m
n
y
=
0
\frac{d^{2} y}{d x^{2}}-(m+n) \frac{d y}{d x}+m n y=0
d
x
2
d
2
y
−
(
m
+
n
)
d
x
d
y
+
mn
y
=
0
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