Which is the explicit formula?

Step-by-step explanation:

From the information given:

y' = y - x²

y' - y = -x²  

This is a first-order linear differential equation of the form y' + p(x)y = q(x)

Thus, y is dependent and x is said to be the independent variable.

xy' = 2y

This is also a first-order linear differential equation with y as the dependent variable and x as the independent variable.

x'' + 5x = e⁻ˣ

This is a second order non-linear differentiall equation.

Here, x is the dependent variable, and since the independent variable is not given, we will take t as the independent variable.

Equation       independent     dependent      order           linear/non linear

                     variable             variable    

y' = y - x²           x                         y                      1                  linear

xy' = 2y              x                         y                     1                   linear

x'' + 5x - e⁻ˣ       t                          x                      2                non-linear

Why this is true for (c) i.e. being non-linear is that; in the above two first-order linear differential equations, we will notice that the dependent variables and their derivatives are not multiplied together, but in the third equation e⁻ˣ which is not the first degree, the case is different as