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suchintan mondal Grade: 12
        

dy/dx +(1/x)  tan y = (1/x2)tany.siny

8 years ago

Answers : (1)

Ramesh V
70 Points
										

dy/dx +(1/x)  tan y = (1/x2)tany.siny


divide the eqn. by tan y.sin y


so eqn comes to be


(1/tan y.sin y)*dy/dx + 1/ x.sin y = 1/x2


put 1/sin y = t


(-cosy / sin2y)*dy/dx = dt/dx


on substituting,we get


-dt/dx + t/x = 1/x2

 or dt/dx - t/x = -1/x2


which is of form dy/dx +P(x).y = Q(x)  with P(x) = -1/x and  Q(x) = -1/x2


solution is t.eintegral P(x) = integral ( Q(x)*eintegral P(x))dx +C


soln is:


t .e -lnx-1/x2 .e -lnx dx


t/x = 1/2x2 +C


i.e., 1/x. sin y = 1/(2x2) +C

8 years ago
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