On transformations of functional-differential equations - dml 2025

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Mathematica features two functions for solving ODEs: DSolve and NDSolve. DSolve is used when the user wishes to find the general function or functions which solve the differential equation, and NDSolve is used when the user has an initial condition.
The differential transform method obtains an analytical solution in the form of a polynomial. It is different from the traditional high order Taylors series method, which requires symbolic competition of the necessary derivatives of the data functions.
Roughly speaking, a functional differential equation, or FDE, is a differential equation for which x(t) depends not only on x(t) but also on the past history of the function s x(s) for ⩽ t . A precise formulation will be given later.
Differential Equations is a vital chapter in the JEE Mains 2025 syllabus. Questions from this topic often require a deep understanding of both theory and problem-solving techniques. Its one of the tough topics in Math for IIT JEE Mains, but with the right preparation, you can master it and score well in the exam.