$$x y^{(4)} + 2 y'' + (x y')^5 = x^3$$
Could someone please explain how this is a fourth order equation? I would have thought it was a second order equation. Does the $4^{th}$ power on the $y$ make a difference?
Order of this differential equation and why?
2
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ordinary-differential-equations
derivatives
pde
notation
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2$y^{(4)}$ means $y''''$, it is a shorthand. – 2017-01-18
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1As Moo states, when the superscript is a natural number in parentheses, they almost always mean that derivative. Notice that the $x^3$ is *not* $x^{(3)}$, for example. – 2017-01-18
1 Answers
0
$y^{(4)}$ is equal to the $4^{\text{th}}$ derivative of $y$.
So, the order of this equation is $4$.