Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2015MathematicsDifferential EquationsActual

The differential equation of the family of circles passing through the origin and having centres on the x -axis is

Options

  1. A2 x y d y d x =x^2-y^2
  2. B2 x y d y d x =y^2-x^2
  3. C2 x y d y d x =x^2+y^2
  4. D2 x y d y d x +x^2+y^2=0

Correct answer

B. 2 x y d y d x =y^2-x^2

Step-by-step solution

Eq. of family of circles passing through the origin & having centres on the x -axis is: aligned & x^2+y^2+2 g x=0 & 2 x+2 y d y d x +2 g=0 & g=- [x+y d y d x ] aligned [on differentiating] Putting the value of (g) in eq. (1) we get; 2 x y d y d x =y^2-x^2

Practice Differential Equations on Quantrex Academy →

More from Differential Equations

Passage: Consider the differential equation e^ x+y dy dx =e^ x-y . Question: What is d^2y dx^2 ( dx dy )^2 equal to ? 2026What is the solution of the differential equation ( dy dx )=p when y(0)=q ? 2026Passage: Consider the differential equation e^ x+y dy dx =e^ x-y . Question: What is the solution of the differential equation with y(0)=0 ? 2026What is the degree of the differential equation ( d^2y dx^2 )^ 3 2 = ( dy dx )^ 5 2 ? 2025If k is an arbitrary constant, then what is the general solution of the equation (x + y)^2 dy dx = k^2 ? 2025Consider the following statements: I. y = xe^ 2x is the solution of dy dx = y (2 + 1 x ) . II. y = x |x| + cx is the solution of dy dx = x + y x . Which of the statements given abo 2025What are the order and degree respectively of the differential equation 2- ( d y d x )^2 ^ 0.6 = d^2 y d x^2 ? 2024Paragraph: Let y d x+ (x-y^3 ) d y=0 be a differential equation. Question: What is the solution of the differential equation? 2024 Full Differential Equations list All NDA PYQs