Question: Solve the following SDEs using the general integrating factor method with (X_{0}=0) : (a) (d X_{t}=frac{X_{t}}{t} d t+sigma t X_{t} d B_{t}), (b) (d X_{t}=X_{t}^{alpha}+sigma

Solve the following SDEs using the general integrating factor method with $X_{0}=0$ :

(a) $d X_{t}=\frac{X_{t}}{t} d t+\sigma t X_{t} d B_{t}$,

(b) $d X_{t}=X_{t}^{\alpha}+\sigma X_{t} d B_{t}$. For what values of $\alpha$ the solution of the equation explodes (is equal to $\infty$ or $-\infty$ for a finite time $t$ ).

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