JEE Main 2024 Mathematics question

The solution of the differential equation (x² + y²)dx − 5xy dy = 0, y(1) = 0 is :

Answer: (A)

Solution

dy/dx = (x² + y²)/(5xy). Put y = vx: v + x dv/dx = (1 + v²)/(5v), so x dv/dx = (1 − 4v²)/(5v) and ∫5v dv/(1 − 4v²) = ∫dx/x. So

Create a free account to read the complete working, and practise questions like this in a timed test.

Question ID VK-016551