BVP of ODE
BVP of ODE
BVP of ODE
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<strong>BVP</strong> <strong>of</strong> <strong>ODE</strong> 11Then z(t) = u(t) + 2t − 7, andu ′′ = z ′′ = [5z − 10t + 35 + sin(3z − 6t + 21)]e t= [5(u + 2t − 7) − 10t + 35 + sin(3(u + 2t − 7) − 6t + 21)]e t= [5u + sin(3u)]e tThe system is transformed to⎧⎨u ′′ (t) = [5u + sin(3u)]e t⎩u(0) = u(1) = 0Example 3 Reduce the following two-point boundary-value problem⎧⎨y ′′ = y 2 + 3 − x 2 + xy⎩y(3) = 7, y(5) = 9to a homogeneous system.Department <strong>of</strong> Mathematics – NTNU Tsung-Min Hwang December 20, 2003
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