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BITSAT 2013
Exam
BITSAT
Year
2013
Subject
Mathematics
Chapter
Differential Equations

BITSAT 2013 · Mathematics · Differential Equations

The general solution of the differential equation (d y)/(d x)+...

The general solution of the differential equation dydx+sin⁡(x+y)=sin⁡(x−y)\frac{d y}{d x}+\sin (x+y)=\sin (x-y) is

Options

  1. Alog⁡tan⁡y+sin⁡x=C\log \tan y+\sin x=\mathrm{C}
  2. Blog⁡tan⁡y2+2sin⁡x=C\quad \log \tan \frac{y}{2}+2 \sin x=\mathrm{C}
  3. Ctan⁡y2+log⁡sin⁡x=C\tan \frac{y}{2}+\log \sin x=\mathrm{C}
  4. DNone of these

Correct answer

B. log⁡tan⁡y2+2sin⁡x=C\quad \log \tan \frac{y}{2}+2 \sin x=\mathrm{C}

Step-by-step solution

The equation is, dydx=sin⁡(x−y)−sin⁡(x+y)=2cos⁡xsin⁡(−y)⇒dysin⁡y+2cos⁡xdx=0⇒∫cos⁡ecydy+2∫cos⁡xdx=C⇒log⁡tan⁡y2+2sin⁡x=C\frac{d y}{d x}=\sin (x-y)-\sin (x+y)=2 \cos x \sin (-y)\Rightarrow \frac{d y}{\sin y}+2 \cos x d x=0\Rightarrow \int \cos e c y d y+2 \int \cos x d x=\mathrm{C}\Rightarrow \log \tan \frac{y}{2}+2 \sin x=\mathrm{C}
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