Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsDifferential EquationsPractice

A curve in the first quadrant is such that the slope of O P is twice the slope of the tangent drawn at P to the curve, where O is the origin and P is any general point on the curve. If the curve passes through 4 , 2 , then its equation is

Options

  1. Ay = x 2 - 14
  2. By 2 = x
  3. Cy = x 3 - 62
  4. Dy = sin ⁡ x - 4 + 2

Correct answer

B. y 2 = x

Step-by-step solution

Slope of O P = 2 d y d x P ⇒ y x = 2 d y d x ⇒ 2 ∫ d y y = ∫ d x x ⇒ 2 ln ⁡ y = ln ⁡ x + ln ⁡ c ⇒ y 2 = c x As it passes through 4 , 2 ⇒ c = 1 ∴ the equation of the curve is y 2 = x

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 NTA Abhyas JEE Main PYQs