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Mathematics
Mathematics
Problem
The general solution of the differential equation,
y
′
+
y
ϕ
′
(
x
)
−
ϕ
(
x
)
⋅
ϕ
′
(
x
)
=
0
y' + y\phi'(x) - \phi(x) \cdot \phi'(x) = 0
y
′
+
y
ϕ
′
(
x
)
−
ϕ
(
x
)
⋅
ϕ
′
(
x
)
=
0
where
ϕ
(
x
)
\phi(x)
ϕ
(
x
)
is a known function is - (A)
y
=
c
e
−
ϕ
(
x
)
+
ϕ
(
x
)
−
1
y = ce^{-\phi(x)} + \phi(x) - 1
y
=
c
e
−
ϕ
(
x
)
+
ϕ
(
x
)
−
1
(C)
y
=
c
e
−
ϕ
(
x
)
−
ϕ
(
x
)
+
1
y = ce^{-\phi(x)} - \phi(x) + 1
y
=
c
e
−
ϕ
(
x
)
−
ϕ
(
x
)
+
1
(B)
y
=
c
e
ϕ
(
x
)
+
ϕ
(
x
)
+
K
y = ce^{\phi(x)} + \phi(x) + K
y
=
c
e
ϕ
(
x
)
+
ϕ
(
x
)
+
K
(D)
y
=
c
e
−
ϕ
(
x
)
+
ϕ
(
x
)
+
K
y = ce^{-\phi(x)} + \phi(x) + K
y
=
c
e
−
ϕ
(
x
)
+
ϕ
(
x
)
+
K
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