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

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)

MP
Answered by Matthew P. Further Mathematics tutor

14921 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the general solution to the differential equation: d^2y/dx^2 - 8 dy/dx +16y = 2x


Let E be an ellipse with equation (x/3)^2 + (y/4)^2 = 1. Find the equation of the tangent to E at the point P where x = √3 and y > 0, in the form ax + by = c, where a, b and c are rational.


Find the values of x where x+3>2/(x-4), what about x+3>2/mod(x-4)?


How far is the point (7,4,1) from the line that passes through the points (6,4,1) and (6,3,-1)?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences