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

The solution for (y+ycos(x)y)dx+(x+xcos(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 cos (x) y) d x + (x + x cos (x) y) d y = 0

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

Solution steps

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

Solve separable ODE:

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

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

(2 + x) y^{^{'}} - y = 0

x (1 + y^{2}) d x - y (1 + x^{2}) d y = 0

\frac{d x}{d t} = 125 - \frac{x}{100}

\frac{d Q}{d t} = 4 Q^{2} ln (t), Q (1) = - 1

\frac{d p}{d t} = t^{2} p - p + t^{2} - 1

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