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

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 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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