Unformatted text preview: n.
b) Use this to solve the ODE x2 y 00 + 3xy 0 3 y = 0. c) Use the variation of parameters method to solve the equation x2 y 00 +3xy 0
3y = .
x AMATH 350
Due Friday, November 12
1. Consider a system of two second order ODEs:
y + a1 ( x ) y + a2 ( x ) y = f ( x )
z + b1 ( x ) z + b2 ( x ) z = g ( x )
By introducing the variables u1 = y, u2 = y , u3 = z, u4 = z , show that
this can be written as a ﬁrst order system
u1 ( x )
u2 ( x )
u3 ( x )
u4 ( x ) u = A(x)u + F(x) where u(x) = , A(x) is an appropriately deﬁned matrix valued function and F(x) is an
appropriately deﬁned vector valued func...
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This document was uploaded on 02/09/2014.
- Winter '14