Explain-the method of characteristic curves

Question

Solving Partial Differential Equations by Change of Variables and Characteristic Curves

Solve the following problem:

In solving this problem, derive the general solution of the given equation by using an appropriate change of variables.

1. ∂u/∂t - 2 ∂u/∂x = 2

In this exercise,

(a) solve the given equation by the method of characteristic curves, and

(b) check you answer by plugging it back into the equation.

2. ∂u/∂x + x² ∂u/∂y = 0