Solve the differential equation (1 + x^2)dy/dx = x tan(y)

Firstly rearrange the equation so that only dy/dx is on the left hand sidedy/dx = (x/(1+x^2)) tan(y)Now separate the variables such that the x terms are on one side with the dx, and the y terms are on the other side with the dy. Now we can place integral signs on both sides.∫ 1/tan(y) dy = ∫ (x/(1+x^2)) dx
Now use the identity cot(y) = 1/tan(y)
∫ cot(y) dy = ∫ (x/(1+x^2)) dx
Now integrate both sides and remember to include the constant of integration, the '+c'
ln |sin(y)| = (1/2)ln |1+x^2| + c

Answered by Christian G. Maths tutor

5566 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I integrate 4x*exp(x^2 - 1) with respect to x?


What is the tangent line to the curve y = x^3+4x+5 at the point where x = 2?


(Core 3 level) Integrate the function f(x) = 2 -cos(3x) between the bounds 0, pi/3.


Show that Sec2A - Tan2A = (CosA-SinA)/(CosA+SinA)


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