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As an Introduction, differential equations are broadly divided into two categories: Ordinary Differential Equations (ODE) and Partial Differential Equations (PDE). An Ordinary Differential Equation (ODE) is defined as an equation that involves derivatives of one or more dependent variables with respect to only one independent variableae:T456,Now I'm thinking through how to generate this PDF with all 54 images—I need to read each one, extract the questions, write comprehensive solutions that tie back to the course material, and produce a polished final document. I'm considering the best approach for this environment: HTML with embedded image URLs and MathJax for rendering math, then converting to PDF through a headless browser seems most practical given the available tools. I'll organize the image reading by batches and start pulling the unseen files from the context paths, then systematically work through identifying which images contain assignments and which are just notes before building out the HTML document with embedded images and solutions. I need to read through 36 unseen images across the three batches to gather the full course content, then organize everything into an HTML structure grouped by topic—starting with first and second-order ODEs in the early batches, moving through solution methods like separation of variables and undetermined coefficients, and finishing with PDEs and Laplace transforms in the final 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I'll wait for the next update."}]}}],["p",{},["text",{},"Second batch received — that's "],["strong",{},["text",{},"18 more images"]],["text",{}," (course notes covering the course outline, ODE definitions and classification, formation of ODEs from relations, separation of variables with worked examples and assignments, second-order homogeneous ODEs with the auxiliary equation and D-operator, the three root cases, undetermined coefficients with polynomial/trig/eigenfunction combinations, and variation of parameters with its assignment)."]],["p",{},["text",{},"Still holding off on any analysis as agreed."]],["p",{},["strong",{},["text",{},"Progress: 36 / 58 uploaded."]],["text",{}," Please go ahead with your third and final batch, then confirm when everything is up so I can start building the 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working through batch 3, which contains 18 images from WA0044 to WA0061, bringing the total count to 54 rather than the expected 58. I'm noting down brief descriptions of the content—it looks like PDE notes covering subsidiary equations and related concepts—and I'll report this progress once I have confirmation."}]}}],["p",{},["text",{},"Third batch received — that's "],["strong",{},["text",{},"18 more images"]],["text",{}," (partial differential equations: formation of PDEs from arbitrary functions, Lagrange's method with subsidiary equations, the \"one variable held fixed\" and \"ratio & proportion\" methods with fully worked examples and assignments; plus Laplace transforms: transforms of tⁿ, sinh/cosh, the shift theorem, multiplication by tⁿ, inverse Laplace transforms including completing the square, with examples and assignments)."]],["p",{},["strong",{},["text",{},"Progress: 54 / 58 uploaded."]]],["p",{},["text",{},"That leaves 4 images remaining by my count. 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