Solve the following initial-value problem, showing all work, including a clear general solution as well as the particular solution requested (label the gen. sol. and particular write both solutions in explicit form (solved for y). x dy/dx = x^3 + 2y subject to: y(2) = 6

General Solution is and the particular solution is  

Step-by-step explanation:

This is a linear diffrential equation of type

..................(i)

here

The solution of equation i is given by

we have

Thus the solution becomes

This is the general solution now to find the particular solution we put value of x=2 for which y=6

we have

Thus solving for c we get c = -1/2

Thus particular solution becomes

answer: i could not see part the question so ill explain how to get the answer

step-by-step explanation: for instance the distance she travele d is 10 and she traveled the same amout each mile so do 10 divided by how many miles she drove each time and you ge your answer.

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.