COMEDK · Maths · 32. Differential Equations
\(\text { The general solution of the differential equation }(1+\tan y)(d x-d y)+2 x d y=0 \text { is }\)
- A \(y(\sin x+\cos x)=\sin x+c e^{-x}\)
- B \(x(\sin y+\cos y)=\sin y+c e^{-y}\)
- C \(x(\sin y+\cos y)=\sin y+c e^y\)
- D \(y(\sin x+\cos x)=\sin x+c e^x\)
Answer & Solution
Correct Answer
(B) \(x(\sin y+\cos y)=\sin y+c e^{-y}\)
Step-by-step Solution
Detailed explanation
The given differential equation is \((1+\tan y)(dx - dy) + 2x dy = 0\). Rearranging the terms to form a linear differential equation in \(x\): \((1+\tan y) dx = (1+\tan y - 2x) dy\) \(\dfrac{dx}{dy} = \dfrac{1+\tan y - 2x}{1+\tan y} = 1 - \dfrac{2x}{1+\tan y}\)…
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