Refer to page 70 for a non-exact differential equation. Solve the equation by finding a suitable integrating factor. Verify the exactness after applying the factor and determine the solution step-by-step. Instructions: Provide only relevant content. Solve step-by-step, clearly showing how the integrating factor is found and applied. All calculations must be detailed and correct. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]

Refer to page 92 for a problem involving the stability of a fixed point in a nonlinear system of ODES. Linearize the system near the fixed point and determine its stability using eigenvalues of the Jacobian matrix. Instructions: Focus strictly on the stability analysis. Clearly outline the steps, including finding the Jacobian, determining eigenvalues, and concluding stability. Show all calculations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]

Refer to page 75 for a problem involving the orthogonality of sine and cosine functions over a given interval. Provide a detailed proof by evaluating the appropriate integrals. Instructions: Provide step-by-step calculations showing the orthogonality proof clearly. Avoid unnecessary content and ensure every step is justified. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]

Let f(z) be the function defined by the formula 1 f(z) = (2-1)(x-2)² (i) Find the Laurent series of f(z) about the point z = 1 that is valid in the region {z = C: |z − 1| > 1}. (ii) Find the Laurent series of f(2) about the point z = region { € C: 0 < | z − 2| < 1}. 2 that is valid in the

Refer to page 84 for a problem requiring evaluation of a triple integral. Convert the integral into spherical coordinates and evaluate step-by-step, showing all necessary transformations and calculations. Instructions: Focus strictly on the problem. Outline the steps clearly, including the coordinate transformation and volume element, and provide all calculations in detail. Irrelevant content is not allowed. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]

Rewrite the equation to solve for T instead of Pout. Pout= - - 8.36 [(1 ) Latin[(1)(1)] 1/2} {(1) 1/2 + (1-T)/2} x {1 - [(1 − )(1 − − T)] 1/2} -

I need expert solution using Drawing 2A ,2B and 2C then solv

Refer to page 74 for a non-homogeneous differential equation. Solve it using the method of variation of parameters. Outline each step clearly, including finding the complementary solution and particular solution. Instructions: Focus on solving the problem only. Provide a detailed step-by-step solution, show all calculations, and avoid irrelevant explanations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]

A surface integral problem can be found on page 88. Use Stokes' Theorem to convert the surface integral into a line integral. Solve it step-by-step, ensuring that all vector field and curve calculations are clearly shown. Instructions: Provide only relevant steps. Outline the problem, apply Stokes' Theorem, and show all vector field and integral calculations without skipping steps. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]