Question

solve the initial value problem

Answer 1

\[\frac{ d }{ dc }=x \left( 6+x ^{2} \right)^{6}, y(0)=0\]

Answer 2

is it really d/dc?

Answer 3

uh dy/dx sorry

Answer 4

you want to put all the y terms on one side and all the x terms on the other

Answer 5

dy = x(6+x^2)^6 dx

Answer 6

what next?

Answer 7

\[\int\limits_{}^{} dy = \int\limits_{}^{} x (6 + x^{2})^{6}dx\]

Answer 8

i would integrate this by parts. letting u = x and dv = (6+x^2)^6 dx

Answer 9

so this has to be integrated?

Answer 10

yes. in order to find the solution y(x)

Answer 11

\[y=\frac{ 1 }{ 14 }(6+x ^{2})^{7}\]

Answer 12

yes :).

+ C

C is obtained with [and is unique to] the initial condition given in the question y(0) = 0

Answer 13

so is c 0 or does it have a value? -139968/7

Answer 14

yes. and the solution would be the entire thing written out

Answer 15

so its 0?

Answer 16

my bad. read too fast. it's not 0. its the second thing

Answer 17

+139968/7

Answer 18

are u sure i have one answer that is just the equation i put earlier and then another that is the same but with a minus (-139968/7)

Answer 19

at the end

Answer 20

it is - 139968/7

Answer 21

\[y=\frac{ 1 }{ 14 }(6+x ^{2})^{7}-\frac{ 139968 }{ 7}\]

Answer 22

yes sir

Answer 23

are you super sure??

Answer 24

yes

Answer 25

ok thanks

Answer 26

glad i could help