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Home » Mark (√) against the correct answer in the following: The solution of the DE is A. B. C. D. none of these
Mark (√) against the correct answer in the following: The solution of the DE \frac{\mathrm{dy}}{\mathrm{dx}}+y \log y \cot x=0 is
A. \cos x \log y=C
B. \sin x \log y=\mathrm{C}
C. \log y=\mathrm{C} \sin x
D. none of these
CBSE | Class 12 | Linear Differential Equations | Maths | RS Aggarwal
Mark (√) against the correct answer in the following: The solution of the DE \frac{\mathrm{dy}}{\mathrm{dx}}+y \log y \cot x=0 is
A. \cos x \log y=C
B. \sin x \log y=\mathrm{C}
C. \log y=\mathrm{C} \sin x
D. none of these

Solution:

\frac{d y}{d x}+y \log y \operatorname{Cot} x=0
Let \log \mathrm{y}=\mathrm{t}
On differentiating we get
\begin{array}{l} \frac{1}{y} d y=d t \\ \frac{d t}{t}=-\operatorname{Cot} x d x \\ \log t=-\log (\sin x)+C \\ \log t+\log (\sin x)=C \\ \log (\operatorname{tsin} x)=C \\ t \sin x=C \\ (\log y)(\sin x)=C \end{array}
Therefore, (\log y)(\sin x)=C is the solution of given equation.

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