# Thread: is there lenear euqation that..

1. ## is there lenear euqation that..

doesnt have constant coefficients?

2. Originally Posted by transgalactic
doesnt have constant coefficients?
Yes.

As long as you have (for lack of a better term) a "polynomial DE" of the form

$\displaystyle f_n(x) \frac{d^ny}{dx^n} + f_{n - 1}(x) \frac{d^{n - 1}y}{dx^{n - 1}} + f_{n - 2}(x) \frac{d^{n - 2}y}{dx^{n - 2}} + \dots + f_2(x)\frac{d^2y}{dx^2} + f_1(x) \frac{dy}{dx} + f_0(x) y = f(x)$.

In other words, as long as the coefficients are nothing more than functions of x, the equation is still linear.

3. can you give an example of some thing which is not a function of x?

4. E.g.

$\displaystyle x^2\frac{d^2y}{dx^2} + 3x^4\frac{dy}{dx} + 7xy = 8\sin{x}$.

Do you see that the coefficients are nothing more than functions of x?

5. can you give an example of non lenear equation?

6. Originally Posted by transgalactic
can you give an example of non lenear equation?
$\displaystyle \frac{d^2y}{dx^2} + 3x\sin{y}\frac{dy}{dx} + 6y = 0$.

Can you see how the coefficient of $\displaystyle \frac{dy}{dx}$ is "more than" a function of $\displaystyle x$? It has a function of $\displaystyle y$ in it as well.

7. yes i understand thanks