#275 There are times when the coefficient

There are times when the coefficient  - Math

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There are times when the coefficient p(x) in a linear equation may not be continuous, but may have a jump discontinuously. Fortunately, we may still obtain a reasonable solution. Consider the initial value problem: dy/dx  + p(x)y = x, y(0) = 1, where

p(x) = (1, 0<=x<=2,

  (3, x>2

a) Find the general solution for 0<=x<=2.

b) Choose constant in the solution of part (a) so that the initial condition is satisfied.

c) Find the general solution for x > 2

d) Now choose the constant in the solution of part (c) so that the solution from part (b) and the solution from part (c) agree at x=2. By patching the two solutions together in this way we obtain a continuous function that satisfies the differential equation except at x=2, where its derivative is undefined.

(e) Sketch a graph of the solution from x = 0 to x = 5.

(Subject: Differential Equation)

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