Question

Write the following first-order differential equations in standard form. y'=x^{3}y+\sin x

First order differential equations
ANSWERED
asked 2021-05-26
Write the following first-order differential equations in standard form. \(\displaystyle{y}'={x}^{{{3}}}{y}+{\sin{{x}}}\)

Expert Answers (1)

2021-05-27

The standart form for a first order linear differential equation is given by
\(y'+p(x)y=q(x)\)
we have \(\displaystyle{y}'={x}^{{{3}}}{y}+{\sin{{\left({x}\right)}}}\)
\(\displaystyle{y}'-{x}^{{{3}}}{y}={\sin{{\left({x}\right)}}}\)
where \(\displaystyle{p}{\left({x}\right)}=-{x}^{{{3}}}\) and \(q(x)=\sin(x)\)

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