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

15682 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Calculate the distance of the centre of mass from AB and ALIH of the uniform lamina.


The equation of a line is y=3x – x^3 a) Find the coordinates of the stationary points in this curve, stating whether they are maximum or minimum points b) Find the gradient of a tangent to that curve at the point (2,4)


Differentiate tan^2(x) with respect to x


How can you integrate the function (5x - 1)/(x^(3)-x)?


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