📐 Mathematics · Differential Equations · JEE

The complementary function of (D² - 3D + 2)y = e^3x (D = d/dx) involves:

Answer: e^x and e^2x.

A e^x and e^2x
B e^3x
C sin x and cos x
D e^-x and e^-2x

Correct answer: A. e^x and e^2x

Explanation: Auxiliary: m² - 3m + 2 = 0, (m-1)(m-2) = 0. m = 1, 2. CF = Ae^x + Be^2x.

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 →

The complementary function of (D² - 3D + 2)y = e3x (D = d/dx) involves:

Concept context

More Differential Equations questions

The complementary function of (D² - 3D + 2)y = e^3x (D = d/dx) involves: