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It’s a fact that Taylor series can be used to study approximate solutions to non-linear ODEs....

Its a fact that Taylor series can be used to study approximate solutions to non-linear ODEs. Use this fact to study approximIt’s a fact that Taylor series can be used to study approximate solutions to non-linear ODEs. Use this fact to study approximate solutions to d 2x dt2 + sin x = 0, (1) subject to x(0) = 0 and x 0 (0) = x1 ≥ 0. Discuss conditions under which your reasoning is accurate, and make sure to include everything you can say. Make choices for x1 to illustrate your points ONLY; make sure to address the problem in full generality in a separate conclusive paragraph.

It's a fact that Taylor series can be used to study approximate solutions to non-linear ODEs. Use this fact to study approximate solutions to d²x + sin 2 0, (1) dt2 subject to x(0) = 0 and x'(0) = x1 > 0. Discuss conditions under which your reasoning is accurate, and make sure to include everything you can say. Make choices for Xi to illustrate your points ONLY; make sure to address the problem in full generality in a separate conclusive paragraph.
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dx X (0) = 24 + sina = o x(0) = 0, at 80 let a(t) = { anth n-1 x(t) = Enant nz n-2 En(n-dant n=2 using sinx= x- tas 3] जा anComparing coefficient of t 20 ast az o 6 olo o 20 as 291 6 as = = 60 ai 60 Com pasing coefficient of t 4 Зоа, тач 3 a, az o 6

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