Find the equation of the curve passing through the point whose differential equation is,
Given, the differential equation of the curve passing through the point ( 0 , π 4 ) is sin x cos y d x + cos x sin y d y = 0 .
Simplify the above equation.
sin x cos y d x + cos x sin y d y = 0 { sin x cos y d x + cos x sin y d y cos x cos y } = 0 ( tan x d x + tan y d y ) = 0
By integrating both sides of the above equation, we get
log ( sec x ) + log ( sec y ) = log C log ( sec x sec y ) = log C { sec x sec y } = C (1)
Substitute x = 0 and y = π 4 in the above equation,
1 × 2 = C
Substitute the value C = 2 in the equation (1).
sec x sec y = 2 sec x × 1 cos y = 2 cos y = sec x 2
Therefore, the above equation is required equation of curve.
Given, the differential equation of the curve passing through the point
Simplify the above equation.
By integrating both sides of the above equation, we get
Substitute
Substitute the value
Therefore, the above equation is required equation of curve.
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