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Solving the Equation Mxy dx + Nxy dy 0
An Existence Theorem
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2xy dy algebra assume auxiliary equation axis called CHAPTER coefficients complementary function Consequently convergent series converges converges absolutely defined definition Denote derivative determine discussion dx dy dy dx dy/dx elimination equa exact EXERCISES Find EXERCISES Solve existence theorem family of curves Find a primitive Find the differential Find the equation following equations form a fundamental formula fundamental system given Hence homogeneous equation integrating factor interval Laplace transform linear differential equation linear equation linearly independent Lipschitz condition matrix method of successive numbers obtained orthogonal trajectories p-discriminant parabolas partial differential equation particular solution power series problem proof proved root satisfies second order Section simultaneous equations singular solution solutions of 14 student Substitute successive approximations Suppose surface system of solutions tangent tank tion variables are separated vector velocity write Wronskian y2 dx yi and y2 yields zero