Sun The sun is the center of the solar system, it is a star, a hot ball of glowing gases. Supply To furnish organs, tissues or cells with a vital element as blood or never fibers. Support To keep going, to uphold. Surroundings The circumstances, conditions or objects by which one is surrounded.
1. Solving Differential Equations (DEs). A differential equation (or DE) contains derivatives or differentials. Our task is to solve the differential equation. This will involve integration at some point, and we'll (mostly) end up with an expression along the lines of  y = ....
Linear vs nonlinear differential equation. Linear differential equations are those which can be reduced to the form $Ly = f$, where $L$ is some linear operator. Your first case is indeed linear, since it can be written as: $$\left(\frac{d^2}{dx^2} - 2\right)y = \ln(x)$$ While the second one is not. To see this first we regroup all $y$ to one side: $$y(y'+1) = x - 3$$