If \( y(t) \) is a solution of the equation \( (1+t) \frac{d y}{d t...

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If \( y(t) \) is a solution of the equation \( (1+t) \frac{d y}{d t}-t y=1 \) and \( y(0)=-1 \) then \( y(1) \) is
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(a) \( -\frac{1}{2} \)
(b) \( e+\frac{1}{2} \)
(c) \( e-\frac{1}{2} \)
(d) \( \frac{1}{2} \)
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