148_pdfsam_math 54 differential equation solutions odd

148_pdfsam_math 54 differential equation solutions odd -...

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Chapter 3 Starting with x = x 0 =0and y = y 0 = 0, we compute F =0+3cos(0 · 0) = 3 ; G =0+0 . 2+3cos[(0+0 . 2)(0 + 0 . 2 { 0+3cos(0 · 0) } )] 3 . 178426 . Using these values, we fnd on Step 4 that x . 2=0 . 2 , y . 1(3 + 3 . 178426) 0 . 617843 . With these new values oF x and y , we repeat the Step 3 and obtain F =0 . 2+3cos(0 . 2 · 0 . 617843) 3 . 177125 ; G . 2+0 . 2+3cos[(0 . . 2)(0 . 617843 + 0 . 2 { 0 . . 2 · 0 . 617843) } )] 3 . 030865 . Step 4 then yields an approximation oF the solution at x . 4: x . . . 4 , y . 617843 + 0 . 1(3 . 177125 + 3 . 030865) 1 . 238642 . By continuing in this way, we obtain Table 3-C.
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