Misc 8 - Chapter 9 Class 12 Differential Equations

Transcript

Misc 8 Find the equation of the curve passing through the point 0 , 4 whose differential equation is sin cos + cos sin =0 sin x cos y dx + cos x sin y dy = 0 sin x cos y dx = cos x sin y dy sin cos = sin cos Integrating both sides sin cos = sin cos sin sin = sin sin = log = + log + log = c log . = Put values of u and v. log cos . cos = c Since the curve passes through 0, 4 Putting x = 0 and y = 4 in (1) log cos 0 .cos 4 = log 1. 1 2 = C = log 1 2 Substitute value of C in (2) log cos cos = log cos . cos = log 1 2 cos x. cos y = 1 2 cos y = 1 2 cos cos y =