Question

Solve the following differential equation : xe^(y/x) − y + x(dy/dx) = 0

An equation involving derivatives of the dependent variable with respect to the independent variables is called a differential equation. A differential equation of the form dy/dx = F(x, y) is said to be homogeneous if F(x, y) is a homogeneous function of degree zero, whereas a function F(x, y) is a homogenous function of degree n if F(λx, λy) = λⁿ F(x, y). To solve a homogeneous differential equation of the type dy/dx = F(x, y) = g(y/x), we make the substitution y = vx and then separate the variables.

An equation involving derivatives of the dependent variable with respect to the independent variables is called a differential equation. A differential equation of the form dy/dx = F(x, y) is said to be homogeneous if F(x, y) is a homogeneous function of degree zero, whereas a function F(x, y) is a homogenous function of degree n if F(λx, λy) = λⁿ F(x, y). To solve a homogeneous differential equation of the type dy/dx = F(x, y) = g(y/x), we make the substitution y = vx and then separate the variables. Based on the above, answer the following questions:

Solve the differential equation : x dy/dx = y – x tan(y/x)