Question

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

First order differential equations
ANSWERED
asked 2021-05-22
Write the following first-order differential equations in standard form. \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{t}\right.}}}}={y}{x}{\left({x}+{1}\right)}\)

Answers (1)

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 \(q(x)=0\)

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