Answer pleeeas

(3.1) … … …

Multiply the right side by x/x :

Substitute y(x) = x v(x), so that dy/dx = x dv/dx + v :

This DE is now separable. With some simplification, you get

Now you're ready to integrate both sides (on the left, the denominator makes for a smooth substitution), which gives

Solve for v, then for y (or leave the solution in implicit form):

(3.2) … … …

It may help to recognize this as a Bernoulli equation. Multiply both sides by :

Substitute , so that . Then you get a linear equation in z, which I write here in standard form:

Multiply both sides by an integrating factor, , which gives

and lets us condense the left side into the derivative of a product,

Integrate both sides:

Solve in terms of y :

(3.3) … … …

This DE is exact, since

are the same. Then the general solution is a function f(x, y) = C, such that

Integrating both sides of the first equation with respect to x gives

Differentiating this result with respect to y then gives

Then the general solution is

Given that y (1) = 4, we find

so that the particular solution is

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

sadsdda

step-by-step explanation: