Help! a) Solve the first order linear differential equation \frac{dy}{dx}+xy=x,\ y_0=-6.

Monique Slaughter

Monique Slaughter

Answered question

2022-01-20

Help!
a) Solve the first order linear differential equation dydx+xy=x, y0=6. b) Write down any two applications of first order linear differential equation.

Answer & Explanation

Annie Gonzalez

Annie Gonzalez

Beginner2022-01-20Added 41 answers

a) The given differential equations is,
dydx+xy=x
where, y0=6
Now,
dydx=xxy
 dydx=x(y1)
 dyy1=xdx
Integrating we have,
log|y1|==x22+A, A in integrating constant.
Given y0=6
So,
log|61|=0+A
 A=log|7|
Therefore, the solution is,
log|y1|+x22=log|7|
 logy17=x22
 y17=ex22
 y1=7ex22
The rewquired solution is,
y=17ex22
einfachmoipf

einfachmoipf

Beginner2022-01-21Added 32 answers

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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