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.
d^4y / dm^4 = y (3 - 8m) / m(5 - 7y)

Answer 1

Answer:

- The differential equation is an Ordinary Differential Equation

- It is of the fourth order

- The dependent variable is "y"

- The independent variable is "m"

- It is nonlinear

Step-by-step explanation:

d^4y / dm^4 = y (3 - 8m) / m(5 - 7y)

- This is an Ordinary Differential Equation (ODE) because it contains ordinary derivatives of the dependent variable with respect to the independent variable.

- It is of the fourth order because the highest derivative of the dependent variable with respect to the independent variable is 4, that is d^4y/dm^4

- The dependent variable is "y"

- The independent variable is "m"

- It is nonlinear because the equation contains the product of the dependent variable with its derivatives.

The equation can be written as

5md^4y/dm^4 - 7yd^4y/dm^4 = y (3 - 8m)

and

7yd^4y/dm^4 make the equation nonlinear.