1 t y" (t) + -y' (t) 1 + t² 1 + t² verify that y₁ (t) = √√1+ t² is a solution. Then use Theorem 8 on page 198 to find y₂2 (t). Note that you may" d t 1 need to use the fact that (1 + t²)³/2 ·y(t) = = 0. Directly dt √1+t² Then, find a particular solution to t 1 y" (t) + ₁ + t²Y (t) y' 1 variation of parameters. 1 + t2 y(t) = 2 1 + t² by the

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