Consider the IVP below: dy dx (a) (b) y1/3 where y(0) = 1 State the largest open x-y region on which the appropriate Existence/Uniqueness Theorem applies. Justify your answer, and be sure to mention which theorem you are using! Find the solution to this IVP. Then, state the x-interval on which the solution is actually valid. Justify your answer.

Find all singular points of the given equation and determine whether each one is regular or irregular. (x + 2)°(x – 5)y" + 3(x – 5)y/ – 2(x + 2)y = 0 | Number of singular points: |Choose one▼

Let f(x) = 30- Find the critical points c that correspond to local minima. (Use symbolic notation and fractions where needed. Give your answer the form of a comma separated list. Enter DNE if there are no critical points.) Find the critical points c that correspond to local maxima. (Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. Enter DNE if there are no critical points.) Find the values at which the points of inflection occur. (Use symbolic notation and fractions where needed. Give your answer the form of a comma separated list. Enter DNE if there are no inflection points.) Determine the interval on which f is concave up. (Use symbolic notation and fractions where needed. Give your answer as interval in the form (*, *). Use the symbol ∞o for infinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[", "]" depending on whether the interval is open or closed. Enter Ø if the interval is empty.) XE…