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TS EAMCET · Maths · Differential Equations

The solution of dydx=1-y2, y0=1, is

  1. A sin-1y=x-sin-11
  2. B sin-1y=x+sin-11
  3. C cos-1y=x+cos-11
  4. D sin-1y+x=sin-11
Verified Solution

Answer & Solution

Correct Answer

(B) sin-1y=x+sin-11

Step-by-step Solution

Detailed explanation

dydx=1-y2 ⇒dy1-y2=dx ⇒∫dy1-y2=∫dx ⇒sin-1y=x+C Put x=0, y=1 ⇒sin-11=C ⇒C=sin-11 So, solution is, sin-1y=x+sin-11