Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202224 Jun 2022Morning ShiftMathematicsDifferential EquationsActual

If x = x y is the solution of the differential equation y d x d y = 2 x + y 3 y + 1 e y , x 1 = 0 ; then x e is equal to

Options

  1. Ae e e 3 - 1
  2. Be 3 e e - 1
  3. Ce e - 1
  4. De e e 2 - 1

Correct answer

B. e 3 e e - 1

Step-by-step solution

Given d x d y - 2 x y = y 2 y + 1 e y Finding integrating factor I . F . = e ∫ − 2 y d x = e − 2 ln y = 1 y 2 ⇒ x y 2 = ∫ y + 1 e y d y ⇒ x y 2 = y · e y + C 0 = e + C ⇒ C = - e ⇒ x y 2 = y e y - e Putting y = e in the equation we get ⇒ x e 2 = e . e e - e ⇒ x = e 3 e e - 1

Practice Differential Equations on Quantrex Academy →

More from Differential Equations

Let y : (- , ) (0, ) be the solution of the differential equation dy dx = e^ 5x y^3 + y^3 e^x + e^x y^4 , satisfying y(0) = 1 2 . Then the value of y( _e 2) is 2026Let y = f(x) be the real valued function defined on the interval (0, ) , satisfying y(1) = 0 and the differential equation x dy dx = y - x^3 . Then which of the following statement 2026Let y=y(x) be the solution of the differential equation x 1-x^2 ,dy + (y 1-x^2 - x ⁻¹x )dx = 0 , x (0, 1) , _ x 1^- y(x) = 1 . Then y ( 1 2 ) equals: 2026Let y = y(x) be the solution of the differential equation (x^2 - x x^2 - 1 )dy + (y(x - x^2 - 1 ) - x)dx = 0 , x 1 . If y(1) = 1 , then the greatest integer less than y( 5 ) is ___ 2026Let y = y(x) be the solution of the differential equation ( x)^ 1/2 ,dy = ( ^3 x - ( x)^ 3/2 y) ,dx , 0 < x < 2 , y ( 4 ) = 6 2 5 . If y ( 3 ) = 4 5 , then ^4 equals _______. 2026Let y = y(x) be the solution of the differential equation x ( y x )dy = (y ( y x ) - x )dx , y(1) = 2 and let = ( y(e¹²) e¹² ) . Then the number of integral values of p , for which 2026Let y=y(x) be the solution of the differential equation: dy dx + ( 6x^2+(3x^2+2x^3+4)e^ -2x (x^3+2)(2+e^ -2x ) )y=2+e^ -2x , x (-1,2) , satisfying y(0)= 3 2 . If y(1)= (2+e⁻²) , th 2026Let y = y(x) be the solution of the differential equation dy dx = (1 + x + x^2)(1 - y + y^2) , y(0) = 1 2 . Then (2y(1) - 1) is equal to: 2026 Full Differential Equations list All JEE Main PYQs