Solve the differential equation e^x dx+(e^x cot(y)+2y csc(y))dy=0.
M=e^x
N=e^x cot(y)+2y csc(y)
My=0
Nx=e^x cot(y)
Obviously isn't exact.
What to do next?
Solve the differential equation e^x dx+(e^x cot(y)+2y csc(y))dy=0.
M=e^x
N=e^x cot(y)+2y csc(y)
My=0
Nx=e^x cot(y)
Obviously isn't exact.
What to do next?
Multiply your equation by siny. You will obtain:
e^{x} sinydx + e^{x}cosy dy + d(y ^{2}) = 0
or
d(e^{x} siny) + d(y^{2}) = 0
Thus, your solution is
e^{x} siny + y^{2} = const (y is not equal to zero)