Teaching MPPSC Assistant Professor Mock Test Series 2025 Physical Sciences Mathematical Methods of Physics
Solve the homogeneous linear differential equation: \( \frac{d^2y}{dx^2} + \frac{dy}{dx} + y = (\log x) \sin(\log x) \).
1
\( y = C_1 \cos(\log x) + C_2 \sin(\log x) - \frac{1}{4} [(\log x)^2 \cos(\log x) + (\log x) \sin(\log x)] \)
2
\( y = C_1 \cos(\log x) + C_2 \sin(\log x) - \frac{1}{4} [(\log x)^2 \cos(\log x) - (\log x) \sin(\log x)] \)
3
\( y = C_1 \cos(\log x) + C_2 \sin(\log x) - \frac{1}{4} [(\log x)^2 \sin(\log x) - (\log x) \cos(\log x)] \)
4
\( y = C_1 \cos(\log x) + C_2 \sin(\log x) - \frac{1}{4} [(\log x)^3 \cos(\log x) - (\log x) \sin(\log x)] \)