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dy/dx +(1/x) tan y = (1/x 2 )tany.siny

dy/dx +(1/x)  tan y = (1/x2)tany.siny

Grade:12

1 Answers

Ramesh V
70 Points
12 years ago

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

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