MHT CET202411 May 2024Morning ShiftMathematicsDifferential EquationsActual
The general solution of d y ~d x + ( x+y 2 )= ( x-y 2 ) is
Options
- A( y 2 )= C -2 x
- B( y 4 )= C -2 ( x 2 )
- C( y 2 + 4 )= C -2 x
- D( y 2 + 4 )= C -2 ( x 2 )
Correct answer
B. ( y 4 )= C -2 ( x 2 )
Step-by-step solution
aligned & d y ~d x + ( x+y 2 )= ( x-y 2 ) & d y ~d x = ( x-y 2 )- ( x+y 2 ) & d y ~d x =-2 ( y 2 ) ( x 2 ) aligned Integrating on both sides, we get aligned & cosec ( y 2 ) d y=- 2 ( x 2 ) d x+ c ₁ & ( y 4 ) 1 2 =- 2 ( x 2 ) 1 2 + c ₁ & ( y 4 )=C-2 ( x 2 ), where C= 1 2 c₁ aligned