Allied & ICAR Exam Bank • ALLIED_0081 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Higher order linear ODEs with constant coefficients

Question Statement:

The general complementary function of $\frac{d^2 y}{dx^2} - 5\frac{dy}{dx} + 6y = 0$ is $C_1 e^{2x} + C_2 e^{k x}$. The value of $k$ is:

Answer Key:

3

Step-by-Step Solution & Explanation

$m^2 - 5m + 6 = 0 \implies (m - 2)(m - 3) = 0 \implies m = 2, 3$. Thus $k = 3$.
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