Solve the differential equation dy/dx = y/x(x + 1) , given that when x = 1, y = 1. Your answer should express y explicitly in terms of x.

Rearrange differential equation to get 1/x(x+1) dx = 1/y dy. Separate x side into partial fractions where 1/x(x+1) = 1/x - 1/(x+1). Integrate each side. Resulting equation involves natural logs. Substitute in boundary conditions (known values of x and y) to find a value for the integration constant. Simplify the equation on the x side using standard log rules. Raise e to the power of each side of the equation to remove natural logs. Hence, y=2x/(x+1).

Answered by Alexander T. Maths tutor

15690 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is the derivative of y = (3x-2)^1/2 ?


Integrate x^2e^x with respect to x between the limits of x=5 and x=0.


Given that y = 5x^3 + 7x + 3, find dy/dx


Why, how and when do we use partial fractions and polynomial long division?


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