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Mathematics
Problem
Consider the differential equation
d
y
d
x
=
x
cos
x
1
+
e
y
\displaystyle \frac{dy}{dx}=\frac{x\cos x}{1+e^{y}}
d
x
d
y
=
1
+
e
y
x
cos
x
. Which of the following implicit relations is a correct general solution? a)
e
y
−
y
=
x
sin
x
+
cos
x
+
C
e^{y}-y=x\sin x+\cos x+C
e
y
−
y
=
x
sin
x
+
cos
x
+
C
b)
y
+
e
y
=
x
sin
x
−
cos
x
+
C
y+e^{y}=x\sin x-\cos x+C
y
+
e
y
=
x
sin
x
−
cos
x
+
C
c)
y
+
e
y
=
x
sin
x
+
cos
x
+
C
y+e^{y}=x\sin x+\cos x+C
y
+
e
y
=
x
sin
x
+
cos
x
+
C
d)
e
y
+
y
=
sin
x
+
x
cos
x
+
C
e^{y}+y=\sin x+x\cos x+C
e
y
+
y
=
sin
x
+
x
cos
x
+
C
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