+91-8076753736 [email protected]

-->

Differential Equations

Question

Wired Faculty App

Solve:
$straight x dy over dx plus 2 straight y space equals space straight x squared log space straight x$

Solution

The given differential equation is

straight x dy over dx plus 2 straight y space equals space straight x squared space logx

or

dy over dx plus 2 over straight x straight y space equals space straight x space logx

Comparing it with

dy over dx plus Py space equals space straight Q comma space space we space get comma space space straight P space equals space 2 over straight x comma space space straight Q space equals space straight x space log space straight x

therefore space space space integral straight P space dx space equals space 2 space integral 1 over straight x dx space equals space 2 space log space straight x. space straight e to the power of integral straight P space dx end exponent space equals space straight e to the power of 2 space log space straight x end exponent space equals space straight e to the power of log space straight x squared end exponent space equals space straight x squared

Solution of given differential equation is

straight y space straight e to the power of integral straight P space dx end exponent space equals space integral straight Q space straight e to the power of integral straight P space dx end exponent dx plus straight c

or

straight y. straight x squared space equals space integral straight x space log space straight x. space straight x squared space dx plus straight c

or space space straight x squared. straight y space equals space integral left parenthesis log space straight x right parenthesis. space straight x cubed space dx space plus straight c or space space straight x squared straight y space equals space left parenthesis log space straight x right parenthesis. space straight x to the power of 4 over 4 minus integral 1 over straight x. straight x to the power of 4 over 4 dx plus straight c or space space space straight x squared straight y space equals space straight x to the power of 4 over 4 log space straight x space minus space 1 fourth integral straight x cubed space dx plus straight c or space space space straight x squared straight y space equals space straight x to the power of 4 over 4 log space straight x minus space 1 fourth. space straight x to the power of 4 over 4 plus straight c or space space space straight y space equals straight x squared over 4 log space straight x space minus space 1 over 16 straight x squared plus straight c space straight x to the power of negative 2 end exponent space is space the space required space solution. space

Some More Questions From Differential Equations Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation