📐 Mathematics · Differential Equations · JEE

For d²y/dx² - 5dy/dx + 6y = 0 with roots m = 2, 3, the general solution:

Answer: y = Ae²ˣ + Be³ˣ.

A y = Ae²ˣ + Be³ˣ
B y = (A+Bx)e²ˣ
C y = A sin 2x + B cos 3x
D y = Ae^x + Be^6x

Correct answer: A. y = Ae²ˣ + Be³ˣ

Explanation: Two distinct real roots m₁=2, m₂=3: y = Ae^m₁x + Be^m₂x = Ae²ˣ + Be³ˣ.

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.

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Equations involving derivatives and their solutions

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For d²y/dx² - 5dy/dx + 6y = 0 with roots m = 2, 3, the general solution:

Concept context

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