Write the equation in the form y′=f(y/x) then use the substitution y=xu to find an implicit general solution. Then solve the initial value problem.

y′=5y2+4x2xy, y(1)=3

The resulting differential equation in x x and u u can be written as xu′= which is separable.
Separating variables we arrive at du=dx/x
Separating variables and and simplifying the solution can be written in the form u2+1=Cf(x) where C is an arbitrary constant and f(x)= .
Transforming back into the variables x and y and using the initial condition to find C we find the explicit solution of the initial value problem is y = .

i can try and you the very best that i can.

addition

step-by-step explanation:

the total estimated nappy use.=10,500,000

step-by-step explanation:

given that on an average the average baby uses 3528 napkins.

in a particular year 2014, the number of births were 299697 in new south wales.

rounding off the number of births to the nearest hundred thousand we have

no of birtsh = 300000

also rounding off the average usage to nearst thousand we get

average use of a baby = 3500

hence total number of nappy estimated to be used = 3500x300000

= 10,500,000

answer is 10,500,000 nappies

step by step solution :

step   1   :

1.1     4 = 22

(4)3 = (22)3 = 26

equation at the end of step   1   :

  ((23) • 26)2

step   2   :

equation at the end of step   2   :

  (23 • 26)2

step   3   :

final result :

  218

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