y" + arctan(y) = 7
is this differential equation linear or non linear?
nonlinear
better review what an LDE is.
why is it nonlinear?
google is your friend.
Surely your text also has a section on linear DE's, and states what they are.
To determine whether a differential equation is linear or non-linear, we check the highest power of the dependent variable (in this case, y) and its derivatives.
In the given equation, we have y" + arctan(y) = 7. Here, y" represents the second derivative of y. The term arctan(y) involves the dependent variable y itself. Since y appears in a non-linear function, which is arctan(y), this differential equation is classified as a non-linear differential equation.
To summarize, the given equation y" + arctan(y) = 7 is a non-linear differential equation.