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I honestly tried, but I could not wrap my head around what they mean by 'Maclaurin series for y'; much less how they found y considering the only other information given was:

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I first used integration, but then... am I supposed to substitute all values for y with 0 in order to obtain the maclaurin series? idk, it all seemed quite foreign to be. Help please?

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Since it's given $y=1$ when $x=0$, we have $$y(x)=y(0)+y'(0)x+\frac{1}{2}y''(0)x^2 + ...$$ $$=1+x+\frac{x^2}{2}+....$$

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