Explain the basic concepts ordinary and partial differential equations (ODEs, PDEs), order, general and particular solutions, initial value problems (IVPs). Give examples.

What are the steps of solving an ODE by the Laplace transform?

What kinds of problems lead to ordinary differential equations? To partial differential equations?

In Problems find the general solution of each given system of differential equations and sketch the lines in the direction of the eigenvectors. Indicate on each line the direction in which the solution would move if it starts on that line.

How do you create equations and use them to solve problems?

Determine which of the following differential equations are separable. Do not solve the equations. $y^{\prime}-x y=0$

Solve the differential equations. $y^{\prime}=e^{x} y^{3}$

Determine which of the following differential equations are separable. Do not solve the equations. $y^{\prime}=x / y$

Solve the differential equations. $y^{\prime}=e^{x} y^{2}$

Solve the differential equations. $y^{\prime}=\frac{y}{x}, x, y>0$

What is the linearization of a system of nonlinear differential equations?

Determine which of the following differential equations are separable. Do not solve the equations. $y^{\prime}=y$

For each of the following differential equations in Problems find all singular points. Determine if these points are regular or irregular. $(2 x+1) x^{2} y^{\prime \prime}-(x+2) y^{\prime}+2 e^{x} y=0$

Determine which of the following differential equations are separable. Do not solve the equations.

(a) $y^{\prime}=y$