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Arnold's Trivium
1991 Arnold's Trivium
81
Problem 81
Problem 81
Source:
July 1, 2010
function
integration
abstract algebra
calculus
Problem Statement
Find the Green's function of the operator
d
2
/
d
x
2
−
1
d^2/dx^2-1
d
2
/
d
x
2
−
1
and solve the equation
∫
−
∞
+
∞
e
−
∣
x
−
y
∣
u
(
y
)
d
y
=
e
−
x
2
\int_{-\infty}^{+\infty}e^{-|x-y|}u(y)dy=e^{-x^2}
∫
−
∞
+
∞
e
−
∣
x
−
y
∣
u
(
y
)
d
y
=
e
−
x
2
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