Find the particular solution of the following differential equation: ​ (x + 2y^2) dy/dx = y, when x = 2, y = 1 ​

Question

Find the particular solution of the following differential equation:

(x + 2y²)\(\cfrac{dy}{dx}\) = y, when x = 2, y = 1

Answer 1

This is the linear differential equation of the form

\(\therefore\) the solution of (1) is given by

This is the general solution.

When x = 2, y = 1, we have

2 = 2(1)² + c(1)

∴ c = 0

∴ the particular solution is x = 2y².