Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Confused! kindly explain, - Ordinary Differential Equations - BITSAT

The solution of the differential equation x\frac{d^{2}y}{dx^{2}}=1, given that y=1, \: \: \frac{dy}{dx}=0, \: when \: x=1, is

  • Option 1)

    y=x\log x+x+2

  • Option 2)

    y=x\log x-x+2

  • Option 3)

    y=x\log x+x

  • Option 4)

    y=x\log x-x

 

Answers (1)

best_answer

 

Solution of Differential Equation -

\frac{\mathrm{d}y }{\mathrm{d} x} =f\left ( ax+by+c \right )

put

 Z =ax+by+c

 

 

- wherein

Equation with convert to

\int \frac{dz}{bf\left ( z \right )+a} =x+c

 

 

 

 x\frac{d^{2}y}{dx^{2}}=1\\ \frac{d^{2}y}{dx^{2}}=\frac{1}{x}\\

Integrating both sides

 \frac{dy}{dx}=logx+c\\ \\0=log1+c\Rightarrow\ c=0\\ \therefore \frac{dy}{dx}=logx\\ \int dy=\int logxdx\\ y=xlogx-x+c\\ 1=1.log1-1+c=c-1\\ c=2\\ \therefore y=xlogx-x+2


Option 1)

y=x\log x+x+2

This option is incorrect 

Option 2)

y=x\log x-x+2

This option is correct 

Option 3)

y=x\log x+x

This option is incorrect 

Option 4)

y=x\log x-x

This option is incorrect 

Posted by

prateek

View full answer

Similar Questions

Trending Articles/News

anam-khan

BITSAT iteration 1 result 2025 out on bitsadmission.com; confirm allotment by July 14
anam-khan

BITSAT 2025 preference editing window open till July 5 for BE, BPharm, MSc admission
anam-khan

BITSAT cut-off for BE Computer Science slightly drops, increases for all others; session 2 result soon

Latest Question