Solve the differential equation dy/dx=(y^(1/2))*sin(x/2) to find y in terms of x.

Here, we must first rearrange our equation so all x terms are on one side and all y terms are on the other. Multiplying both sides by dx and diving both by y^(1/2) gives us y^(-1/2)dy = sin(x/2)dx, which is a directly integrable equation. Integrating both sides, we get 2y^(1/2) = -2cos(x/2) + c, where c is some arbitrary constant of integration. Rearranging to find y, we get y=(-2cos(x/2) + A)^2, where A=c/2.

Answered by Alex J. Maths tutor

6458 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is the method used for differentiation?


Given that y = exp(2x) * (x^2 +1)^(5/2), what is dy/dx when x is 0?


Integrate 2x^3 -4x +5


Integrate, with respect to x, xCos3x


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