1.

Solve sin–1 [dy/dx] = x + y.

Answer»

dy/dx = sin (x + y) 

x + y = t 

1 + (dy/dx) = dt/dx

(dt/dx) – 1 = sin t 

dt/dx = 1 + sin t 

dt/(1 + sin t) = dx 

Integrating both sides we get

∫ dt/(1 + sin t) = ∫ dx 

∫ (1 − sin t/(cos2 t)) dt = x + c 

∫ sec2 t dt – ∫ tan t.sec t dt = x + c 

tan t – sec t = x + c ⇒ tan (x + y) – sec (x + y) = x + c


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