What is the solution for (dy)/y+ye^{cos(x)}sin(x)dx=0 ?

The solution for (dy)/y+ye^{cos(x)}sin(x)dx=0 is y=-1/(e^{cos(x))+c_{1}}

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(dy)/y+ye^{cos(x)}sin(x)dx=0

\frac{d y}{y} + y e^{c o s (x)} sin (x) d x = 0

y = - \frac{1}{e ^{c o s (x)} + c _{1}}

Solution steps

\frac{d y}{y} + y e^{c o s (x)} sin (x) d x = 0

Solve separable ODE:

y = - \frac{1}{e ^{c o s (x)} + c _{1}}

y = - \frac{1}{e ^{c o s (x)} + c _{1}}

cos^{2} (y) sin (x) d x + sin (x) cos (x) d y = 0

\frac{d y}{d x} = 2 x^{4} y, y > 0

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

\frac{d y}{d x} = 2 x cos^{2} (y), y (0) = \frac{π}{4}

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

What is the solution for (dy)/y+ye^{cos(x)}sin(x)dx=0 ?
The solution for (dy)/y+ye^{cos(x)}sin(x)dx=0 is y=-1/(e^{cos(x))+c_{1}}