Question
Solve the following differential equations:
$\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}$
$\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}$
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| $X = x_i$ | $0$ | $1$ | $2$ | $3$ |
| $P(X = x_i)$ | $2k^4$ | $3k^2 - 5k^3$ | $2k - 3k^2$ | $3k - 1$ |