Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20254 Apr 2025Evening ShiftMathematicsDifferential EquationsActual

If a curve y=y(x) passes through the point (1, 2 ) and satisfies the differential equation (7 x^4 y-e^x cosec y ) d x d y =x^5, x 1 , then at x=2 , the value of cosy is:

Options

  1. A2 e ^2- e 64
  2. B2 e ^2+ e 64
  3. C2 e ^2- e 128
  4. D2 e ^2+ e 128

Correct answer

C. 2 e ^2- e 128

Step-by-step solution

aligned & d y d x = 7 y x - e^x cosec y x^5 & d y d x = 7 y y x - e^x y x^5 & y d y d x - y 7 x = -e^x x^5 & let - y=t & y d y d x = d t d x aligned aligned & d t d x + 7 t x = -e^x x^5 & I.F. =x^7 & t. x^7=- x^2 e^x d x & cosy x^7=x^2 e^x-2 x e^x d x & cosy x^7=x^2 e^x-2 x e^x+2 e^x+c & x=1, y= 2 , c=-e & cosy = 2 e^2-e 128 & option (3) aligned

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