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Mathematics
Mathematics
Problem
Verify that
A
x
2
+
B
y
2
=
1
Ax^2 + By^2 = 1
A
x
2
+
B
y
2
=
1
is a solution of the differential equation
x
{
y
d
2
y
d
x
2
+
(
d
y
d
x
)
2
}
=
y
d
y
d
x
.
x \left\{ y \frac{d^2 y}{dx^2} + \left( \frac{dy}{dx} \right)^2 \right\} = y \frac{dy}{dx}.
x
{
y
d
x
2
d
2
y
+
(
d
x
d
y
)
2
}
=
y
d
x
d
y
.
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