What is the solution for 5x-5xcos(y)dx+xsin(y)dy=0 ?

The solution for 5x-5xcos(y)dx+xsin(y)dy=0 is y=arccos(e^{-5x-c_{1}}+1)+2pin

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5x-5xcos(y)dx+xsin(y)dy=0

5 x - 5 x cos (y) d x + x sin (y) d y = 0

y = arccos (e^{- 5 x - c_{1}} + 1) + 2 πn

Solution steps

5 x - 5 x cos (y) d x + x sin (y) d y = 0

Solve separable ODE:

y = arccos (e^{- 5 x - c_{1}} + 1) + 2 πn

y = arccos (e^{- 5 x - c_{1}} + 1) + 2 πn

\frac{d y}{d x} = x^{2} y - 3 y + x^{2} - 3

\frac{d y}{d x} = \frac{- 0.8}{cos ( y )}, y (0) = \frac{π}{3}

\frac{sin ( x )}{1 + y} \frac{d y}{d x} = cos (x)

y^{^{'}} = \frac{x y ^{3}}{9}, y (0) = 6

x \frac{d y}{d x} = y + 3

What is the solution for 5x-5xcos(y)dx+xsin(y)dy=0 ?
The solution for 5x-5xcos(y)dx+xsin(y)dy=0 is y=arccos(e^{-5x-c_{1}}+1)+2pin