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JEE Main20246 Apr 2024Evening ShiftMathematicsDifferential EquationsActual

If the solution y(x) of the given differential equation ( e ^y+1 ) x ~d x+ e ^y x ~d y=0 passes through the point ( 2 , 0 ) , then the value of e ^ y ( 6 ) is equal to_________

Correct answer

0

Step-by-step solution

aligned & ( e ^ y +1 ) x dx + e ^ y x d y =0 & d ( ( e ^ y +1 ) x )=0 & ( e ^ y +1 ) x = C aligned It passes through ( 2 , 0 ) c =2 Now, x= 6 e ^ y =3

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