Best solutions to - "Solve differential equation. dydx=(x+y−1)+x+ylog⁡(x+y)"

sibuzwaW

Answered question

2021-09-26

Solve differential equation.

\frac{d y}{d x} = (x + y - 1) + \frac{x + y}{\log (x + y)}

Answer & Explanation

tabuordy

Skilled2021-09-27Added 90 answers

Step 1 Given

\frac{d y}{d x} = (x + y - 1) + \frac{x + y}{\log (x + y)}

Step 2 solving Differential Equations
Let x+y=v.
Then,

1 + \frac{d y}{d x} + \frac{d v}{d x}

The given differential equation reduces to

\frac{d v}{d x} - 1 = v + \frac{v}{\log v}

\frac{d v}{d x} = v + \frac{v}{\log v}

\frac{\log v}{v (1 + \log v)} d v = d x

On integrating, we get

\int \frac{\log v}{(1 + \log v)} \frac{1}{v} d v = \int 1 . d x + C

\int \frac{t - 1}{t} d t = x + C

Where

t = 1 + \log v

t - \log t = x + C

(1 + \log v) - \log [1 + \log v] = x + C

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?

Product

Company

Connect with us

Get Plainmath App

Google Play

Louki Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus

Cyprus reg.number: ΗΕ 419361

E-mail us: support@plainmath.net

Our Service is useful for:

Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples. Plainmath.net is owned and operated by RADIOPLUS EXPERTS LTD.