2. given that y1 (t) = t3 is a solution of the equation 3t2y"-5ty3y = 0 for t > 0 (1) find a second linearly independent solution y2(t) of (1) solution: we proceed by using the reduction of order method. thus, we need to find a function v such that y2(t) v(t)y1(t) is solution of equation (1). if v not a constant function, then y2 is linearly independent (cf lecture notes). then, 2' vuk and inserting this into equation (1) yields 0 3t("y20'y vy{) 5t (v'yn + vy{) -3vyi 3y" + (6y- 5ty1) (3t°y{ - 5tyh -3y)u 3t°y" 13t', where in the third equality, we used that yi is a solution of (1) and that y1(t) = t3. the last equation is equivalent to 13 0 " for t 0 thus w= v is a solution of the 1st order linear ode 13 for t > 0 3 ct13/3 for t 0 and which (by seperation of variables) has the solution w (t) = any constant c e r. thus, v(t) = u cer and so w(s)ds ct10/3 for t > 0 and any constant y2(t) = v(t)y1(t) = t 10/3 f3 since v is a non-constant function, {yı, y2} is linearly independent for t0

answer:

sometimes

*i think

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.  

-8/2y-8=5/y+4-7y+8/y^2-16

we move all terms to the left:

-8/2y-8-(5/y+4-7y+8/y^2-16)=0

we can not solve this equation