Q13 of 45 Page 1

Solve the following differential equation:

(1 + y2) (1 + log x) dx + x dy = 0

Given, A differential equation (1 + y2) (1 + log x) dx + x dy = 0

To Find: find the solution of given differential equation


Explanation: we have (1 + y2) (1 + log x) dx + x dy = 0


It can be written as:


x dy= - (1 + y2) (1 + log x) dx




Now, Integrate both sides, we get



We know, , then



Now,


let 1 + log x = t , then





Putting the value of t , we get



Hence, This is the solution of given differential equation.


More from this chapter

All 45 →
11

Using properties of determinants, prove the following:

 12

Find the value of a and b such that the following function f(x) is a continuous function:

f (x) = 5 x less than equal to 2 ax+b 2<x<10 21 x geater than or equal to 10

 14

If two vectors vector 9 and vector b are such that | vector a| = 2 , | vector b| = 1 and vector a vector b = 1 then find the value of ( 3 vector a-5 vector b ) ( 2 vector a+7 vector b )

 23

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.