Chapter 1 - Introduction - 1.3 Classification of Differential Equations - Problems - Page 24: 5

5. The equation is a second order nonlinear ordinary differential equation.

5. the equation, $\frac{d^2 y}{dt^2}+ \sin(t+y) = \sin(t)$ is second order because the highest derivative that occurs in it is of the second order; it is nonlinear because the second term in the left-hand side ($\sin(t+y)$) is a nonlinear function; and it is an ordinary differential equation because all the derivatives occuring in the equation (specifically, $\frac{d^2 y}{dt^2}$) are ordinary (not partial) derivatives.