# Second Order DE - Different ways of asking

I'm just wondering, I've come across a Second Order DE Question which says:

Find the general solution of the ODE: $2 \frac {d^2y}{dx^2} + 5 \frac {dy}{dx} − 3y = 0.$

I'm just wondering how this differs from the notes I've seen which use $y''$ I'm thinking that it's the same but I just want to make sure

Thanks

It does not differ at all, it's just a different notation.

It's the same as : $2y'' + 5y' - 3y = 0$

Any derivative of a function, let's say $y(x)$ with respect to $x$, can be written as $y^{(n)} = \frac{d^ny}{dx^n}$. Note that until the third derivative, you use the $'$ notation : $y^{(1)} = y',y^{(2)} = y'', y^{(3)} = y'''$ and for higher derivatives, you use the $y^{(n)}$ notation, where n is the grade of the derivative.

Both of them are notations to show the order of derivative.

You can replace $\frac{d^2y}{dx^2}$ with $y''$. Similarly $\frac{dy}{dx}$ with $y'$.

$2y''+5y'-3y=0$