Solve the following differential equation : x² dy + y(x + y) dx = 0

Method of Separation of Variables for Differential Equations, Homogeneous Differential Equations | PadhAiPro

Question

TextMethod of Separation of Variables for Differential EquationsHomogeneous Differential EquationsCBSE PYQ

Find the particular solution of the differential equation given by x² (dy/dx) – xy = x² cos² (y/(2x)), given that when x = 1, y = π/2.

The differential equation dy/dx = F(x, y) will not be a homogeneous differential equation, if F(x, y) is :

Homogeneous Differential Equations

Find the particular solution of the differential equation given by 2xy + y² – 2x² dy/dx = 0; y = 2, when x = 1.

Find the general solution of the differential equation : y dx = (x + 2y²) dy

The general solution of the differential equation dy/dx = e^(x+y) is :

Find the particular solution of the differential equation dy/dx + sec² x · y = tan x · sec² x, given that y(0) = 0.