AP EAMCET · Maths · Differential Equations
The general solution of the differential equation \(\left(\sin y \cos ^2 y-x \sec ^2 y\right) d y=(\tan y) d x\) is
- A \(\tan y=3 x \cos ^3 y+c\)
- B \(x(\sec y+\tan y)=\cos ^2 y+c\)
- C \(y \sin y=x^2 \cos ^2 y+c\)
- D \(3 x \tan y+\cos ^3 y=c\)
Answer & Solution
Correct Answer
(D) \(3 x \tan y+\cos ^3 y=c\)
Step-by-step Solution
Detailed explanation
Given, differential equation \(\left(\sin y \cos ^2 y-x \sec ^2 y\right) d y=\tan y d x\) \(\Rightarrow \frac{d x}{d y}+\frac{x \sec ^2 y}{\tan y}=\cos ^3 y\) So, I.F. \(=e^{\int \frac{\sec ^2 y}{\tan y} d y}=e^{\ln (\tan y)}=\tan y\) So, solution is given by…
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