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The image you've uploaded contains a list of mathematical problems, mostly focused on solving differential equations. Here’s a transcription and brief overview of the questions I can extract:

**PART-A**
1. Solve \((D + 1)y = 0\).
2. Find the P.I. of \((D^2 + 2) = \sin 2x\).
3. Find the P.I. of \((D^2 + 4) = \cos 2x\).
4. Form a PDE by eliminating the arbitrary constants from \(z = f(xa) + g(y + bt)\).
5. Solve \((D - 1)(D + 1)y = \log x\).

**Module-1: PART-B**
6. Solve \(\frac{d^2y}{dx^2} - 2 \frac{dy}{dx} + y = \cos 3x\).
7. Solve \(3 \frac{d^2y}{dx^2} + 2 \frac{dy}{dx} + 2y = 10(x + 1)\).
8. Solve \((D - 1)(D + 1)y = \log x\).

**Module-2**
9. Solve \(\frac{\partial^2 z}{\partial x^2} = \cos(2x + 3y)\).
10. Solve \(\frac{\partial^2z}{\partial x^2} + z = 0\), given that \(z = e^y\) and \(\frac{\partial z}{\partial x} = 1\) when \(x = 0\).
11. Solve \( \sqrt{p - z} | p + (z - x) q | = (x - y)\).

Would you like a solution for one of these questions? Let me know if you need detailed explanations for any specific problem or further clarifications!

### Follow-up questions:
1. How do you find the complementary function (C.F.) for second-order linear differential equations?
2. What are the steps to eliminate arbitrary constants from a function in PDEs?
3. Can you explain the method to find the particular integral (P.I.) of a non-homogeneous differential equation?
4. How can you solve partial differential equations involving multiple variables?
5. What methods can be used to solve homogeneous versus non-homogeneous differential equations?

### Tip:
When solving differential equations, always check if the equation is homogeneous or non-homogeneous before proceeding to find the complementary function and particular integral.

The image contains various mathematical problems focused on solving differential equations, partial differential equations (PDEs), and particular integrals (P.I.).

This page explains the process of solving ordinary and partial differential equations (PDEs) involving second-order linear equations, complementary functions, and particular integrals. Suitable for engineering and mathematics students.

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