# Identify the following differential equations and hence solve it y=xy'+1-ln y'?

##### 1 Answer

Jul 3, 2018

#### Answer:

General Solution:

# bb( y = c x + 1 - ln c )#

and singular solution:

#y = 2 + ln x#

#### Explanation:

This is in the form of Clairaut's equation:

Differentiate wrt

And factor:

#bbX#

Subbing both

This gives the **general** solution:

#bbY#

Putting that into

This is a **singular** solution.