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).

AT
Answered by Alexander T. Maths tutor

16144 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the stationary points of the curve y (x)= 1/3x^3 - 5/2x^2 + 4x and classify them.


The curve C has equation y = x^3 - 2x^2 - x + 9, x > 0. The point P has coordinates (2, 7). Show that P lies on C.


C and D are two events such that P(C) = 0.2, P(D) = 0.6 and P(C|D) = 0.3. Find P(D|C), P(C’ ∩ D’) & P(C’ ∩ D)


y(x) = x^2(1-x)e^-2x , find y'(x) in the form of g(x)e^-2x where g(x) is a cubic function to be found


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences