what is the order and the degree of the given diff. equation? the given diff. equation is $$y=1+ \frac{dy}{dx}+\frac{1}{2!}\left(\frac{dy}{dx}\right)^2+\cdots+\frac{1}{n!}\left(\frac{dy}{dx}\right)^n$$
it is given that the order is $1$ and the degree is also $1$. But how it happens because the the highest order $1$ has degree is $n$. so how the given degree is possible?

$$e^x=1+\frac{x}{1!}+\frac{x^2}{2!}+\cdots+\frac{x^n}{n!}$$
Hence the given differential equation becomes
 $$y=e^{\frac{dy}{dx}}\quad \Longrightarrow \quad \frac{dy}{dx}=\log y$$
Hence the order and the degree both are $1$.
