Chapter 1 - Introduction - 1.3 Classification of Differential Equations - Problems - Page 24: 2

The order is 2. It is nonlinear.

The differential equation $$(1+y^2)\frac{d^2y}{dt^2} +t\frac{dy}{dt}+y=e^ t $$ has order 2 because the highest derivative appearing in the equation is of order 2. It is nonlinear because the function $y$ is raised to the second power in the term $(1+y^2)\frac{d^2y}{dt^2}$ and because that same term contains a product of $y$ with one of its derivatives.