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Arnold's Trivium
1991 Arnold's Trivium
74
Problem 74
Problem 74
Source:
July 1, 2010
integration
trigonometry
Problem Statement
Sketch the graph of
u
(
x
,
1
)
u(x, 1)
u
(
x
,
1
)
, if
0
≤
x
≤
1
0 \le x\le1
0
≤
x
≤
1
,
∂
u
∂
t
=
∂
2
u
∂
x
2
,
u
∣
t
=
0
=
x
2
,
u
∣
x
2
=
x
=
x
2
\frac{\partial u}{\partial t}=\frac{\partial^2 u}{\partial x^2},\;u|_{t=0}=x^2,\;u|_{x^2=x}=x^2
∂
t
∂
u
=
∂
x
2
∂
2
u
,
u
∣
t
=
0
=
x
2
,
u
∣
x
2
=
x
=
x
2
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