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Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Someone plz tell me what I did wrong

Solve the differential equation

I know there is a rule

but if I let

and the same as y , then substitue , into the original equation , but the answer will be different from applying the rule . I wanna know what's wrong .

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Numbers are the essence of the Universe

harman

Guest

Re: Someone plz tell me what I did wrong

ok if u want to do this by substitution then
put x=sinu
so that dx=cosudu
similarly y=sinv
so that dy=cosvdv
now your eq becomes

=

=

=

Edited to fix the LaTeX

Last edited by mathsyperson (2007-05-31 20:06:04)

harman

Guest

Re: Someone plz tell me what I did wrong

ok if u want to do this by substitution then
put x=sinu
so that dx=cosudu
similarly y=sinv
so that dy=cosvdv
now your eq becomes

=

=

=

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Someone plz tell me what I did wrong

I wanna know what's wrong .

You chose a wrong substitution to use.

And doing the same thing with y gives

Thus

which brings you right back to square one.

When you do integration by substitution, not every substitution will work! Always choose your substitution wisely.

Last edited by JaneFairfax (2007-05-31 21:51:22)

Stanley_Marsh

Member

Registered: 2006-12-13

Posts: 345

Re: Someone plz tell me what I did wrong

thanks  Jane.

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Numbers are the essence of the Universe