Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2012MathematicsDifferential EquationsActual

Let y(x) be a solution of (2+ x (1+y) d y) d x = x . If y(0)=2 , then y ( 2 ) equals

Options

  1. A5 2
  2. B2
  3. C7 2
  4. D3

Correct answer

C. 7 2

Step-by-step solution

Given differential equation is (2+ x (1+y) d y d x = x which can be rewritten as d y 1+y = x 2+ x d x Integrate both the sides, we get aligned & d y 1+y = x d x 2+ x & (1+y)= (2+ x)+ C & 1+y=C(2+ x) & Given y(0)=2 & 1+2=C[2+ 0] C= 3 2 aligned Now, y ( 2 ) can be found as 1+y= 3 2 (2+ 2 ) 1+y= 9 2 y= 7 2 Hence, y ( 2 )= 7 2

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