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Solutions of Differential Equations
First Method of Solution Variables Separable
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apply arbitrary constant arbitrary function change of variable Chap characteristic strip coefficients complete equation compute conical element continuous convergence dependent variable derivatives determine difference dx dy dy _ dy dx dy/dx entries envelope exact exact differential example Exercises.—1 expanded family of curves Find formula geometric given graph Hence homogeneous indicial equation integral curve integral surface integrating factor interpolating function interpolating polynomial interval Legendre polynomials lineal element linear equation linearly dependent Lipschitz condition method of successive multipliers one-parameter family origin orthogonal trajectories partial differential equation particular solution planar element Pn(x polynomial of degree preceding prescribed values problem prove quadratures reduced equation regular singular point replaced roots second member second order Show Simpson's rule singular solution Solve substituting successive approximations tangent tion ui(x velocity whence Wronskian yi(x yn(a yn(x zero