What is the solution for (y+y*cos(x)y)dx+(x+x*cos(x)y)dy=0 ?

The solution for (y+y*cos(x)y)dx+(x+x*cos(x)y)dy=0 is y=(c_{1})/x

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(y+ycos(x)y)dx+(x+xcos(x)y)dy=0

(y + y \cdot cos (x) y) d x + (x + x \cdot cos (x) y) d y = 0

y = \frac{c _{1}}{x}

Solution steps

(y + y \cdot cos (x) y) d x + (x + x \cdot cos (x) y) d y = 0

Solve separable ODE:

y = \frac{c _{1}}{x}

y = \frac{c _{1}}{x}

x^{^{'}} = \frac{- 1}{t} \cdot x - \frac{1}{t}

\frac{d y}{d x} = \frac{x ^{2} - 7}{y ^{2}}, y (0) = 5

y^{2} d y = \frac{2 x + 1}{2 y} d x

sin (x) cos (x) y^{^{'}} - sin (y) cos (x) = 0

y^{^{'}} = \frac{1}{2} (k - y)

What is the solution for (y+y*cos(x)y)dx+(x+x*cos(x)y)dy=0 ?
The solution for (y+y*cos(x)y)dx+(x+x*cos(x)y)dy=0 is y=(c_{1})/x