Question

# Write the following first-order differential equations in standard form. \frac{dy}{dt}=yx(x+1)

First order differential equations
Write the following first-order differential equations in standard form. $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}}={y}{x}{\left({x}+{1}\right)}$$

2021-05-23

The standart form for a first order linear differential equation is given by
$$y'+p(x)y=q(x)$$
we have
$$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={y}{x}{\left({x}+{1}\right)}$$
$$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}-{x}{\left({x}+{1}\right)}{y}={0}$$
where $$\displaystyle{p}{\left({x}\right)}=-{x}{\left({x}+{1}\right)}$$ and $$q(x)=0$$