For problems 9-12, determine two linearly independent power series solutions to the given differential equation cen- tered at x = 0. give a lower bound on the radius of conver- gence of the series solutions obtained. 9. (x^2 – 3)y" – 3xy' - 5y = 0. 10. (1 + x^2)y" + 4xy' + 2y = 0. 11. (1 – 4x^2)y" – 20xy' - 16y = 0. 12. (x^2 - 1)y" – 6xy' +12y = 0.

step-by-step explanation:

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.

165.75 years

p.s. this question was already   asked on/p>

step-by-step explanation: