Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If
y
=
x
x
y = x^x
y
=
x
x
, then prove that
d
2
y
d
x
2
−
1
y
(
d
y
d
x
)
2
−
y
x
=
0
\frac{d^2 y}{dx^2} - \frac{1}{y} \left( \frac{dy}{dx} \right)^2 - \frac{y}{x} = 0
d
x
2
d
2
y
−
y
1
(
d
x
d
y
)
2
−
x
y
=
0
.
Browse the problem library