Question

The differential equation corresponding to the general solution $y = c_{1} + (c_{2}x + c_{3})e^{2x}$ is}

• A. $\frac{d^{2}y}{dx^{2}} - 4\frac{dy}{dx} + 4y = 0$
• B. $\frac{d^{3}y}{dx^{3}} - 4\frac{d^{2}y}{dx^{2}} + 4\frac{dy}{dx} = e^{2x}$
• C. $\frac{d^{3}y}{dx^{3}} - 4\frac{d^{2}y}{dx^{2}} + 4\frac{dy}{dx} = 0$
• D. $\frac{d^{2}y}{dx^{2}} - 4\frac{dy}{dx} + 4y = e^{2x}$

Hint:

A constant $c$ in the solution means 0 is a root. $(Ax+B)e^{kx}$ means $k$ is a repeated root.

Answer 1

The Correct Option is C