Question

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

First order differential equations
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 $$q(x)=\sin(x)$$