Question
Show that the differential equation 
is homogeneous. Find the particular solution of this differential equation, given that x = 0 when y = 1.
Solution
Thus, F(x, y) is a homogeneous function of degree zero. Therefore, the given differential equation is a homogeneous differential equation.
Let x = vy
Differentiating w.r.t. y, we get
Substituting the value of x and
in equation (1), we get
Substituting the value of v, we get
Substituting x = 0 and y = 1 in equation (2), we get
Substituting the value of C in equation (2), we get
which is the particular solution of the given differential equation.
Let x = vy
Differentiating w.r.t. y, we get
Substituting the value of x and
in equation (1), we getSubstituting the value of v, we get
Substituting x = 0 and y = 1 in equation (2), we get
Substituting the value of C in equation (2), we get
which is the particular solution of the given differential equation. 
