In this video explaining problem of solvable for y.This first differentiate separate the variable and integrate then you get general solution.
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Please watch: "Express the f(x) interms of Legendre's polynomials good example find a,b,c & d (PART-2)"
https://www.youtube.com/watch?v=GzkYXT2ibAk
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VTU Engineering Maths 2 Solvable for Y interesting example(PART-4) | NatokHD