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Lecture Notes
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 Massachusetts Institute of Technology
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 18 034  Honors Differential Equations
Honors Differential Equations Documents

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UNIT I: FIRSTORDER DIFFERENTIAL EQUATIONS
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COMPLEX SOLUTIONS AND THE FUNDAMENTAL MATRIX
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An application of the Dirac delta function
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Existence and Uniqueness Theorem
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TERMINOLOGY AND IMPLICIT SOLUTIONS
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LECTURE 13 INHOMOGENEOUS EQUATIONS
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Properties of Hermitian Matrices
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Comments on Hirsch & Smale Chapter 8
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LECTURE 7 MECHANICAL OSCILLATION
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MIT OpenCourseWare http ocw mit edu 18 034 Honors Differential Equations Spring 2009 For information about citing these materials or our Terms of Use visit http ocw mit edu terms 18 034 Recitation February 5th 2009 1 Consider the equation y y 2y For what a is eay a solution Find a solution y0 to y y 2y with exponential growth as x and limx y0 x x 1 2 Suppose that if y0 is a solution to y y 2y F x on all of then there is another solution y1 to the same equation with y1 x y0 x 0 as x 3 Show that y ex and y cos x cannot be solutions of the same rst order equation y f x y on any interval containing the origin 4 Solve ydx 3xdy 14y 4 dy 5 Suppose that a trajectory of 3x2 y dx 3y 2 x dy 0 contains the point 1 1 Show that it also contains the points 1 1 1 1 0 1 1 0 6 Birkho Rota p 6 7 Show that solutions of y g y are convex up or convex down for given y according as g is an increasing or decreasing function there 1
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