What exactly do we mean when say "linear" combination? I've noticed that the term gets abused alot. For instance, suppose I have
$c_1 x_1 + c_2 x_2 = f(x)$...(1)
Eqtn (1) is such what we say "a linear combination of $x_1$ and $x_2$"
In ODE, sometimes when we want to solve a homogeneous 2nd order ODE like $y'' + y' + y = 0$, we find the characteristic eqtn and solve for the roots and put it into whatever form necessary. But in all casses, the solution takes form of $c_1y_1 + c_2y_2 = y(t)$.
The thing is that $y_1$ and $y_2$ itself doesn't even have linear terms, so does it make sense to say $c_1y_1^2 +c_2y_2^2 = f(t)$ is a "quadratic" combination of y_1 and y_2?

I am sure about the linear combination like ODE
In which equation on power of variable involve is and multiplied by any scalar quantity. Such combination is known as linear combination of algebra
