find general solution to: x(dy/dx) + 2y = 4x^2

  • Google+ icon
  • LinkedIn icon
  • 853 views

Divide through by x so:      (dy/dx) +2(y/x) = 4x

Now multiply through by the intergrating factor:  e^(| (2/x) dx) = e^(2.ln(x)) = x^2

so you get:     (x^2)(dy/dx) + 2xy = 4(x^3)

Now integrate the entire equation and you get:        y(x^2) = |(4(x^3))dx = (x^4) + c

Divide through by (x^2) to get the general solution:

y = (x^2) + 4/(x^2)

Matthew P. 11 Plus Maths tutor, GCSE Maths tutor, A Level Maths tutor...

About the author

is an online A Level Further Mathematics tutor with MyTutor studying at Southampton University

Still stuck? Get one-to-one help from a personally interviewed subject specialist.

95% of our customers rate us

Browse tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok