Homogeneous and non-homogeneous equations.
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| Topic | Key Concepts | Typical Weightage | | :--- | :--- | :--- | | | Eliminating constants vs. functions. | Low (Short Questions) | | Lagrange's Method | Solving $Pp+Qq=R$ using subsidiary equations. Multipliers. | High (Compulsory in most exams) | | Non-Linear PDEs | Standard Forms I & II (Clairaut's), Charpit's Method. | Medium | | Separation of Variables | Solving Heat, Wave, and Laplace equations with boundary conditions. | Very High (Long Questions) |
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Partial differential equations are equations that involve an unknown function of multiple variables and its partial derivatives. They are used to model various physical phenomena, such as:
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Modeling sound waves, vibrating strings, and electromagnetic waves. 2. Parabolic PDEs (