Differential Equations

The general solution of the Cauchy-Euler differential equation $x^2 \frac{d^2 y}{dx^2} - 2x \frac{dy}{dx} + 2y = 0$ for $x > 0$ is:

Options:

• (A) y = c_1 x + c_2 x^2
• (B) y = c_1 x^2 + c_2 x^3
• (C) y = c_1 x + c_2 \ln(x)
• (D) y = (c_1 + c_2 \ln x) x^2