A Course in Ordinary and Partial Differential Equations - download pdf or read online

By zalman rubinstein

ISBN-10: 1483230988

ISBN-13: 9781483230986

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Extra info for A Course in Ordinary and Partial Differential Equations

Example text

E) y' = x2 arctan y + ex, f(x, y) = x2 arctan y + ex. /,(*, >01 = i + y 3C2 5 (4 - k)cx - 5c2 = 0, cx - (λ + 2)c2 = 0.

13. Show directly that the solution of the second-order equation y" + a{x)y' + b(x)y = / ( * ) , y(*o) = y°> /(*o) = y1 is unique. Hint: Define z(x) = yx{x) — y2(x), w(x) = z'(x), u(x) = \z(x)\ + \w(x)\ where y1 and y2 are solutions and show that u{x) < c J^o u(t) dt. 46 ORDINARY DIFFERENTIAL EQUATIONS 14. (Minimal and maximal solutions) Suppose D is the infinite strip in the plane defined by a < x < b, - oo ; ο ; (b) /i(x)

This shows that /(x f c _ 1 , /(x f c _ 1 )) and hence j>£(x) are well defined. Furthermore, for xk~1 < x < xk, \\/\x) -f(x,f(x))\\ = \\f(xk-l,y%xk-1)) -/(x,/(x))|| < e since |χ-χ*-1|<δ and ||/(x) - /(x^ 1 )!! ^ - x*"1)

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A Course in Ordinary and Partial Differential Equations by zalman rubinstein


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