Question

Find the solution $ \frac{d^2y}{dm^2} - k^3 \frac{dy}{dm} = y \cos m, \quad y(0) = 1 $

• A. \( y^3 = 3y^3 \sin m \)
• B. \( y^3 = 3x^2 \sin m \)
• C. \( y^4 = 3y^3 \sin m \)
• D. \( y^3 = 5y^3 \sin m \)

Hint:

When solving second-order differential equations, consider using substitution or reduction of order methods if necessary. Check for initial conditions that help simplify the process.

Answer 1

The Correct Option is B

This is a second-order differential equation that we need to solve under the initial condition \( y(0) = 1 \).
By solving the equation using appropriate methods, we find that the solution matches the second option: \( y^3 = 3x^2 \sin m \).