Question:
Solve the differential equation:
\[
\frac{d^2y}{dx^2} + 4y = 0
\]
Solve the differential equation:
\[
\frac{d^2y}{dx^2} + 4y = 0
\]
Show Hint
For second-order linear differential equations with constant coefficients, solve the characteristic equation to find the general solution.
Updated On: Jun 17, 2025
- $y = C_1 \cos(2x) + C_2 \sin(2x)$
- $y = C_1 e^{2x} + C_2 e^{-2x}$
- $y = C_1 e^{x} + C_2 e^{-x}$
- $y = C_1 \cos(x) + C_2 \sin(x)$
Show Solution
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The Correct Option is A
Solution and Explanation
The characteristic equation is: \[ r^2 + 4 = 0 \] \[ r = \pm 2i \] Thus, the general solution is: \[ y = C_1 \cos(2x) + C_2 \sin(2x) \]
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