Solve differential equation. \frac{dy}{dx}=(x+y-1)+\frac{x+y}{\log(x+y)}Z

sibuzwaW

sibuzwaW

Answered question

2021-09-26

Solve differential equation.
dydx=(x+y1)+x+ylog(x+y)

Answer & Explanation

tabuordy

tabuordy

Skilled2021-09-27Added 90 answers

Step 1 Given
dydx=(x+y1)+x+ylog(x+y)
Step 2 solving Differential Equations
Let x+y=v.
Then, 1+dydx+dvdx
The given differential equation reduces to
dvdx1=v+vlogv
dvdx=v+vlogv
logvv(1+logv)dv=dx
On integrating, we get
logv(1+logv)1vdv=1.dx+C
t1tdt=x+C
Where t=1+logv
tlogt=x+C
(1+logv)log[1+logv]=x+C

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?