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If y(x) satisfies the differential equ...

If `y(x)` satisfies the differential equation `y^(prime)-ytanx=2xs e c x` and `y(0)=0` , then

A

`y(pi/4)=pi^(2)/(8sqrt(2))`

B

`y^(')(pi/4)=pi^(2)/18`

C

`y(pi/3)=pi^(2)/9`

D

`y^(')(pi/3)=(4pi)/3+(2pi^(2))/(3sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
A, D
`(dy)/(dx) -ytanx=2xsecx`
`therefore cosx(dy)/(dx) + (-sinx)y=2x`
`therefore d/(dx)(ycosx)=2x`
Integrating, we get
`y(x)cosx=x^(2)+c`, where c=0 since y(0)=0
When `x=pi/4, y(pi/4)= pi^(2)/(8sqrt(2))`
When `x=pi/3, y(pi/3)=(2pi^(2))/9`
When `x=pi/4, y^(')(pi/4)=pi^(2)/(8sqrt(2))+pi/sqrt(2)`
When `x=pi/3, y^(')(pi/3)=(2pi^(2))/(3sqrt(3))+(4pi)/3`
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