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Question Number 55939 by MJS last updated on 06/Mar/19

$$\frac{y^{\prime }}{y}=1-\cot x$$$$y=?$$

Answered by kaivan.ahmadi last updated on 06/Mar/19

$$\frac{1}{y}\frac{dy}{dx}=1-cotx\Rightarrow$$$$\frac{1}{y}dy=(1-cotx)dx\Rightarrow$$$$\int \frac{1}{y}dy=\int (1-cotx)dx\Rightarrow$$$$lny=x-ln\mid sinx\mid \Rightarrow y=e^{x-ln\mid sinx\mid }\Rightarrow$$$$y=\frac{e^x}{\mid sinx\mid }+C$$

Commented by MJS last updated on 06/Mar/19

$$\mathrm{thank}\mathrm{you}$$

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