Question

A differential equation is given. Classify it as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and dependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear. 6d²n/dy²​=5y(1−5y)

Answer 1

The equation 6d²n/dy² = 5y(1-5y) is an ordinary differential equation (ODE) of the second order, with 'y' as the independent variable and 'n' as the dependent variable. The equation is nonlinear.

Step-by-step explanation:

The given differential equation is 6d²n/dy² = 5y(1−5y). This is an ordinary differential equation (ODE) because it involves functions of only one variable and its derivatives with respect to that variable.

The order of the differential equation is determined by the highest derivative present in the equation. Since the highest derivative is the second derivative of n with respect to y, the equation is a second-order differential equation.

In this equation, 'y' is the independent variable and 'n' is the dependent variable, as the value of 'n' depends on 'y'.

Furthermore, the equation is nonlinear, as indicated by the presence of the term 5y(1−5y), which involves a product of the independent variable 'y' and a nonlinear function of 'y' (1−5y), making the equation nonlinear.