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Find A and B so that y=Asin3x+bcos3x sat...

Find `A` and `B` so that `y=Asin3x+bcos3x` satisfies the equation `(d^2y)/(dx^2)+4(dy)/(dx)+3y=10cos3xdot`

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`y=Asin3x+bcos3x`
diff. with respect to x
`dy/dx=Acos3x*3+B(-Sin3x)*3`
diff with respect to x
`(d^2y)/(dx^2)=-9Asin3x-9Bcos3x`
`(d^2y)/(dx^2)+4dy/dx+3y=10`
LHS`=-9Asin3x-9Bcos3x+12Acos3x-12Bsin3x+3Asin3x+3Bcos3x=10cos3x`
`sin3x(-9A-12B+3A)+cos3x(-9B+12A+3B)=10cos3x`
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RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
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  7. If y=e^"tan"^((-1)"x"), prove that (1+x^2)y2+(2x-1)y1=0.

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  11. If y=x+tan x, show that cos^2 x (d^2y)/(dx^2)-2y+2x=0

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  12. If y=e^-x cos x, show that (d^2y)/(dx^2)= 2e^-1 sin x

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  13. If y=log(sinx),"p r o v et h a t"(d^3y)/(dx^3)=2cosxcos e c^3xdot

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  14. If y=x^3logx ,"p r o v et h a t"(d^4y)/(dx^4)=6/xdot

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  15. If y=(logx)/x ,s howt h a t(d^2y)/(dx^2)=(2logx-3)/(x^3)

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  16. If y=2 sin x+3cos x, show that (d^2y)/(dx^2)+y=0

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  17. Find . (d^2y)/(dx^2),ifx=a t^2,y=2a tdot

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  18. If x=sin theta,y=cosptheta,p rov et h a t (1-x^2)y2-x y1+p^2y=0,w ...

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  19. If y=tan^-1x find (d^2y)/(dx^2) in terms of y alone.

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  20. If x^m y^n=(x+y)^(m+n), prove that (d^2y)/(dx^2)=0

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