IIT JEE , AIEEE Forum - Mathematics , Algebra

barsharahul

find the solution of the following differential equation

xy y''+ x (y')² +yy' =0

Greatdreams

Solution is A x² + B y² = 1

or differential equation of all conics whose axes coincide with the axes of co ordinates.

Courtesy : hard disk which rests above shoulders between ears underneath hair......
(I am not bald

)

solve for yourself and get the answer! Trust me dude this is the only way to be able to solve 100 problems in 2 hours.

feynmann

Not so difficult !!

Just put z = yy'

The given eqn is

x ( yy'' + y'^2 ) + yy' = 0

substituting

x dz/dx + z = 0

giving z x =k

or y y' x = k

or yy'= k/x

integrating both sides wrt x

we get the soln as

y^2/2 = k ln x + c

Greatdreams

Look at who's answering .........the potential rank 1 guy !! sorry dada.....haven't ever been able to solve 100 problems together ...in 2 hours ( honest confession ) . I am an ordinary guy.

However ( with a few known problems like these ) went pretty close! + this year 20 objective questions where you need to put in some explanation. + because of leakage, paper should be tougher
( statistics ).

Odds are heavily stacked against us.

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