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Differential Calculus

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17 Sep 2007 23:16:28 IST

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Solve que.

None

Solve The differentiable eq.

dy/dx +y.sec²x = tanx.sec²x

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Ramya Hegde

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Joined: 8 Feb 2007

Posts: 612

18 Sep 2007 05:59:58 IST

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U can compare this with the form,

dy/dx +Py =Q

where integrating factor (I.F) can be found by

I.F= e^ P dx

Hence, for the above differential equation,

I.F. = e^

sec²x dx

= e^tanx

We know,

y(I.F.) = Q. (I.F.) dx

y. e^tanx = e^tanx. tanx. sec²x dx

For, RHS,

take tanx=t

sec²x dx= dt

Hence integral becomes,

RHS= e^t . t dt

On integrating this u'll get,

= e^t(t-1)

putting t=tanx, we get the final expression as,

y. e^tanx = e^tanx(tanx-1) +c

where c is the const. of integration.

Hope u got it!!

Priyesh

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Joined: 18 Feb 2007

Posts: 1042

18 Sep 2007 22:21:33 IST

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Perfect answer ramya

Ramya Hegde

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Joined: 8 Feb 2007

Posts: 612

19 Sep 2007 04:56:18 IST

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thank uuuuuuuuuu

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