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Mathematics
Mathematics
Problem
For the differential equation, general solution for
x
cos
(
y
x
)
(
y
d
x
+
x
d
y
)
=
y
sin
(
y
x
)
(
x
d
y
−
y
d
x
)
,
x \cos\left(\frac{y}{x}\right)(y dx + x dy) = y \sin\left(\frac{y}{x}\right)(x dy - y dx),
x
cos
(
x
y
)
(
y
d
x
+
x
d
y
)
=
y
sin
(
x
y
)
(
x
d
y
−
y
d
x
)
,
(where
c
c
c
is constant of integration) is (A)
x
=
c
y
sec
(
y
x
)
x = cy \sec\left(\frac{y}{x}\right)
x
=
cy
sec
(
x
y
)
(B)
x
y
cos
(
y
x
)
=
c
xy \cos\left(\frac{y}{x}\right) = c
x
y
cos
(
x
y
)
=
c
(C)
x
=
c
y
sec
(
x
y
)
x = cy \sec\left(\frac{x}{y}\right)
x
=
cy
sec
(
y
x
)
(D)
x
y
=
c
⋅
cos
(
y
x
)
xy = c \cdot \cos\left(\frac{y}{x}\right)
x
y
=
c
⋅
cos
(
x
y
)
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