Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202622 January 2026Evening ShiftMathematicsDifferential EquationsActual

If y=y(x) satisfies the differential equation 16( x+9 x )(4+ 9+ x ) y ~d y=(1+2 y) d x, x>0 and y(256)= 2 , y(49)= , then 2 is equal to :

Options

  1. A2( 2 -1)
  2. B3( 2 -1)
  3. C2 2 -1
  4. D2 -1

Correct answer

C. 2 2 -1

Step-by-step solution

y 1+2 y d y= d x 16( 9 x +x )(4+ 9+ x ) 4+ 9+ x =t 1 2 9+ x d x 2 x =1 d x 1 2 n|1+2 y|= 4 d t 16 t +C . 1 2 n|1+2 y|= 1 4 n , 4+ 9+ x +C 1 2 n(2 y+1)= 1 4 n|4+ 9+ x |+C Substituting (256, 2 ) 1 2 n 3= 1 2 n 3+C C=0 Substituting (49, ) 1 2 n (2 +1)= 1 4 n 8 n (2 +1)= 1 2 n 8 n (2 +1)= n 2 2 2 +1=2 2 2 =2 2 -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