2. (5 points) Consider the system x' (Assume det A0). = (i) = x. Find the special values of a for which the phase plane changes type. 3. For each interval above, choose a representative a and sketch the phase portrait.

Find the derivative of the astroid x2/3+y2/3=a2/3.

In a city the number of hours of sunlight on the summer solstice of 2015 was 18.42, and the number if hours of sunlight on the winter solstice was 5.44. (Hint: the summer solstice occurs on the 172nd day of the year and there are 365 days until the next one.)  Find a sinusoidal function of the form y = Asin that models the data.  y = ___sin (___x - ___) + ___

Let f(x,y) = x^2 y + e^xy sin y.   At Point (1,0) State the direction where the function increase/decrease most rapidly and State the direction where the function has no change at Point (1,0).

FIND THE DERIVATIVES NO.1 AND NO. 2

Find general solution of ODE : y'+y=sinx+x

find the oscillation of the difference equation to the determine red in same way of the determine yellow

Find the second order derivatives of the function cos3x

suppose that the length of time between consecutive high tides is 12 hours and 26 mins. on a particular day the high tide occurred at 12:26 am (0.43 hours) and the low tide occurred at 7:07 (7.12 hours). Water heights are measured as the amounts above or below the mean lower low water. The height of the water at high tide was 5.94 feet and the height of the water at low tide was 0.04 feet. The next high tide will occur at 12:52pm. Find the sinusoidal function of the form of sin

find dy y = tan-1(ex2)