|

Integral Calculus

Cool goIITian

 Joined: 24 Apr 2007 Post: 88
16 Mar 2008 23:00:07 IST
0 People liked this
3
523
solve the differial equation
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Integral Calculus

xdy-ydx=[x^2-y^2] dx

Blazing goIITian

Joined: 14 Jan 2007
Posts: 602
16 Mar 2008 23:03:51 IST
0 people liked this

HEY,
PUT Y=XT
X(T+ X DT/DX)=XROOT(1-T^2)

Blazing goIITian

Joined: 20 Jan 2007
Posts: 472
16 Mar 2008 23:50:18 IST
1 people liked this

xdy - ydx = [ ] x^2 + y^2 dx

xdy/dx = y + x^2 + y^2 dx

dy/dx = y/x + 1 + { y/x } ^2

put y = vx

y = v + xdv/dx

v + xdv/dx = v + 1 + v^2

1/ 1+ v^2 dv = (1/x) dx

on itegratin

log(v + 1 + v^2  ) = log x  + C

log ( (y/x)  +  1 + (y/x)^2 )  = logx + logA where A > 0

y/x +  (x^2 + y^2 ) /x  =Ax

y/x +  (x^2 + y^2 )  = Ax^2.

Hot goIITian

Joined: 15 Mar 2008
Posts: 137
17 Mar 2008 12:47:04 IST
0 people liked this

One very easy method:
$x.dy - y.dx = sqrt {x^{2} - y^{2}} .dx$
=> $rac {x.dy - y.dx}{sqrt {x^{2} - y^{2}}} = dx$
Divide both sides by x,
=> $rac { rac {x.dy - y.dx}{x^{2}}}{sqrt {1 - {( rac {y}{x})}^{2}}} = rac {dx}{x}$
Integrating we get,
=> $sin^{ - 1} { rac {y}{x}} = ln{|x|} + C$

 Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a avatar to have your pictures show up by your comment If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

## For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
 Altitude - 16545 m Post - 7958
2. Himanshu
 Altitude - 10925 m Post - 3836
3. Hari Shankar
 Altitude - 9965 m Post - 2186
4. edison
 Altitude - 10815 m Post - 7797
5. Sagar Saxena
 Altitude - 8625 m Post - 8064
 Altitude - 6330 m Post - 1979

Physics

Topics

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone