Question

The differential equation for which \( ax + by = 1 \) is the general solution is:

• A. \( \frac{dy}{dx} = x + c \)
• B. \( y \frac{d^2 y}{dx^2} + x = 1 \)
• C. \( \frac{d^2 y}{dx^2} = 0 \)
• D. \( \frac{d^3 y}{dx^3} = 0 \)

Hint:

For finding differential equations, differentiate the given general solution repeatedly until all arbitrary constants are eliminated.

Answer 1

The Correct Option is C

Step 1: Consider the given general solution: \[ ax + by = 1 \] Differentiating both sides with respect to \( x \): \[ a + b \frac{dy}{dx} = 0 \] Differentiating again: \[ b \frac{d^2 y}{dx^2} = 0 \] Since \( b \neq 0 \), we conclude: \[ \frac{d^2 y}{dx^2} = 0 \]