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Mathematics
Mathematics
Problem
Verify that
y
=
a
e
b
x
y = ae^{bx}
y
=
a
e
b
x
is a solution of the differential equation
d
2
y
d
x
2
=
1
y
(
d
y
d
x
)
2
\frac{d^2y}{dx^2} = \frac{1}{y} \left(\frac{dy}{dx}\right)^2
d
x
2
d
2
y
=
y
1
(
d
x
d
y
)
2
.
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