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📐 Mathematics  ·  Differential Equations  ·  JEE

The complementary function (CF) of a linear DE with constant coefficients is the:

Answer: Solution when right-hand side = 0 (homogeneous part).

  • A Solution obtained directly from the right-hand side forcing term
  • B Solution when right-hand side = 0 (homogeneous part)
  • C The antiderivative of the entire differential equation
  • D The multiplying factor that converts the equation into exact form

Correct answer: B. Solution when right-hand side = 0 (homogeneous part)

Explanation: CF: general solution of the homogeneous equation (RHS = 0). The complete solution = CF + PI (particular integral).

Family of Solution Curves: y = Ax²Each value of the constant A gives ONE particular curve from the family

The general solution y=Ax² represents an entire FAMILY of curves, one for each value of the arbitrary constant A; a particular solution (fixed by an initial condition) selects exactly one curve from this family.

Concept context

Equations involving derivatives and their solutions

Read the full Differential Equations notes →