Question

what does "obtain a family of solutions" mean in differential equations? it's the instruction in our homework and i dont know what that means lol..is it the particular solution and general solution?

Answer 1

it means the answer will have a + constant and therefore isn't just one function but a group of functions known as a family.
ps can you do this for me?
using stokes theorem find the integral of F(x,y,z)=yzi+2xzj+e^xy k where C is the circle x^2+y^2=16 and z=5.

Answer 2

i dont know what that means o.O

Answer 3

that ok, neither do i.

Answer 4

hah lgbas? you want to know?

Answer 5

sure

Answer 6

a family of function happens when you integrate, you know how to integrate correcT?

Answer 7

yeah

Answer 8

alright so say you integrate something super easy like dx

Answer 9

\[\int{}{}dx\]=x+c correct?

Answer 10

yes..so x+ c is the family?

Answer 11

yes because c can be anything say the otherside was dy and you got

y=x+c ... this is a family solution when you draw the family c can be 1,2,3,4,5, basically anything; you get something like this