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...Dierential equations m t nair department of mathematics iit madras contents parti ordinary page number first order ode introduction direction field and isoclines initial value problem linear with variables separated homogeneous exact reducible to or variable separable form second higher constant coecients non system rst power series method the some examples legendre s equation polynomials solution around singular points orthogonality functions sturm liouville slp references lectures for course ma july november an is involving unknown function its derivatives respect independent x f y k here j represents th derivative we shall also denote thus a sometimes above can be put in by mean dened on interval i b which dierentiable satises e example note that every c de r simple shows have more than one fact obtain family parabolas as curves but if require curve pass through certain specied point then may get unique demand given must so this case suppose called integral at each tangent slope pre...