Monique Slaughter

2022-01-20

Help!
a) Solve the first order linear differential equation . b) Write down any two applications of first order linear differential equation.

Annie Gonzalez

Expert

a) The given differential equations is,
$\frac{dy}{dx}+xy=x$
where, ${y}_{0}=-6$
Now,
$\frac{dy}{dx}=x-xy$

Integrating we have,
$\mathrm{log}|y-1|==\frac{{x}^{2}}{2}+A$, A in integrating constant.
Given ${y}_{0}=-6$
So,
$\mathrm{log}|-6-1|=0+A$

Therefore, the solution is,
$\mathrm{log}|y-1|+\frac{{x}^{2}}{2}=\mathrm{log}|-7|$

The rewquired solution is,
$y=1-7{e}^{-\frac{{x}^{2}}{2}}$

einfachmoipf

Expert

b) Here we need to write two applications of first order linear differential equation.
So,two applications of first order linear differential equation is,
(ii) Newtons

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