Final Answer
$y+2\ln\left(y\right)=-\ln\left(\sin\left(x\right)\right)+C_0$
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Step-by-step Solution
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1
Combine all terms into a single fraction with $y$ as common denominator
$\cos\left(x\right)\cdot dx+\frac{y+2}{y}\sin\left(x\right)\cdot dy=0$
Learn how to solve differential equations problems step by step online.
$\cos\left(x\right)\cdot dx+\frac{y+2}{y}\sin\left(x\right)\cdot dy=0$
Learn how to solve differential equations problems step by step online. Solve the differential equation cos(x)dx+(1+2/y)sin(x)dy=0. Combine all terms into a single fraction with y as common denominator. Grouping the terms of the differential equation. x+0=x, where x is any expression. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality.
Final Answer
$y+2\ln\left(y\right)=-\ln\left(\sin\left(x\right)\right)+C_0$