The general solution of the differential equation (x - y^ 2 )dx + y(5x + y^ 2 )dy = 0 is :

JEE Main 2022 Mathematics question

The general solution of the differential equation is :

(1)Correct
(2)
(3)
(4)

Answer: (1)

Solution

dy/dx = ( − x)/(y(5x + )). Let , so 2y dy/dx = dv/dx = 2(v − x)/(5x + v). Put v = kx: k + x dk/dx = 2(k − 1)/(5 + k), so x dk/dx = + 2)/(k + 5) = −(k + 1)(k + 2)/(k + 5).

See the full step-by-step solution

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

Create a free account

Question ID VK-024814