Consider the differential equation (dy/dx)=y^3(2x+3x^2) a)find the general solut

ID: 3289111 • Letter: C

Question

Consider the differential equation (dy/dx)=y^3(2x+3x^2)

a)find the general solution; leave it in implicit form

b) for the arbitrary constant C in your solution, find the value of C corresponding to the Initial Conditions

i) y(1)=1 ii) Y(-1)=1 iii) y(0)=3

c) what are the integral curves corresponding to i) and iii)?

For the differential equation dy/dx+y cot(x)=cos(x)

a) find the solution y(x) for intitial condition y(pi/2)=0 what is the interval of definition of this solution?

b) give an intial condition that would give rise to a solution whih was defined on the interval 3pi<x<4pi

A) (dy/dx)=y^3(2x+3x^2)

or (dy/y^3) = (2x + 3x^2 )dx

or (-1/2)/y^2 = (x^2 + x^3 ) + C ....................(1)

B) (i) y(1) = 1 or -0.5 = 2 + C or C = -5/2

(ii) y(-1) = 1 or -0.5 = 1 - 1 + C or C = -0.5

(iii) y(0)= 3 or 0.5/9 = 0 + 0 + C or C = 1/18