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Mathematics
Mathematics
Problem
If
x
=
a
cos
θ
+
b
sin
θ
x = a \cos \theta + b \sin \theta
x
=
a
cos
θ
+
b
sin
θ
and
y
=
a
sin
θ
−
b
cos
θ
y = a \sin \theta - b \cos \theta
y
=
a
sin
θ
−
b
cos
θ
, then prove that
y
2
d
2
y
d
x
2
−
x
d
y
d
x
+
y
=
0
y^2 \frac{d^2 y}{dx^2} - x \frac{dy}{dx} + y = 0
y
2
d
x
2
d
2
y
−
x
d
x
d
y
+
y
=
0
.
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