# Non-order equation

#### idontknow

$$\displaystyle y^{(1)} y^{(2)}\cdot .... \cdot y^{(n)} =e^{nx} \; \;$$ , $$\displaystyle n\in \mathbb{N}$$ .

Another way to write it better : $$\displaystyle \prod_{i=1}^{n} \frac{d^i y}{dx^i } =e^{nx}$$ .

#### idontknow

Let $$\displaystyle b_{n} =e^{nx}\; \;$$ then $$\displaystyle y^{(n+1)} =\frac{b_{n+1} }{b_n }=e^x$$ .
The equation $$\displaystyle y^{(n+1)} =e^x \;$$ has solution $$\displaystyle y=c+e^x$$.