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

0.16 or 16%

step-by-step explanation:

lets take a coin for example.

if you toss it twice, it has a 1/4 chance of landing on heads both times because 1/2 * 1/2 is 1/4.

with the cards, the chance of picking dog is 0.4. having two people pick one is like picking a card twice in a row. so 0.4 * 0.4 is 0.16, or 16%

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23