how that all solutions of 2y' + ty = 2 approach a limit as t → [infinity]. Hint: Consider the general solution, y = e−t2/4 t 0 es2/4 ds + Ce−t2/4, and use L'Hôpital's rule on the first term. Write the first term of y = e−t2/4 t 0 es2/4 ds + Ce−t2/4 as t 0 es2/4 ds . Use L'Hôpital's rule on the first term: lim t → [infinity] t 0 es2/4 ds = lim t → [infinity] et2/4 = lim t → [infinity] . As t → [infinity] the second term approaches lim t → [infinity] Ce−t2/4 = . As t becomes large, all solutions converge to the function . Find the limiting value.