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