Ex 9.4, 15 - Find equation of curve passing through (0, 0) - Ex 9.4

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  1. Chapter 9 Class 12 Differential Equations
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Ex 9.4, 15 Find the equation of curve passing through the point 0 , 0 and whose differential equation is = sin = sin x = sin x dx = sin x dx Integrating both sides = sin y = sin y = ( ) sin y = ( cos ) ( cos ) y = + cos y = + ( ) cos y = + sin y = + y + y = + 2y = ( sin cos ) y = 1 2 sin cos + C Given curve passes through (0, 0) Putting x = 0, y = 0 in equation 0 = 1 2 0 ( sin 0 cos 0 ) + C 0 = 1 2 (0 1) + C 0 = 1 2 + C C = 1 2 Putting value of C in (1) y = 1 2 sin cos + 1 2 y 1 2 = 1 2 sin cos 2 1 2 = 1 2 ( sin + cos ) 2y 1 = ( + )

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