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Find A\ a n d\ B so that y=Asin3x+Bcos3x...

Find `A\ a n d\ B` so that `y=Asin3x+Bcos3x` satisfies the equation `(d^2y)/(dx^2)+4(dy)/(dx)+3y=10cos3x` .

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`y=A sin 3 x+B cos 3 x`
differentiating w.r.t x
` frac{d y}{d x}=3 A x cos 3 x+3 B(-sin 3 x)`
Again differentiating w.r.t times
...
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  10. If x=2a t , y=a t^2 , where a is a constant, then find (d^2y)/(dx^2...

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  11. If x=f(t) and y=g(t) , then write the value of (d^2y)/(dx^2) .

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  14. If y=|x-x^2| , then find (d^2y)/(dx^2) .

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  15. If y=|(log)e x| , find (d^2y)/(dx^2) .

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  16. If x=acosnt-bsinnt , then (d^2x)/(dt^2) is (a)n^2x (b) -n^2x (c) n x ...

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  17. If x=a t^2,\ \ y=2\ a t , then (d^2y)/(dx^2)= -1/(t^2) (b) 1/(2\ a t^...

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  18. If y=a x^(n+1)+b x^(-n) , then x^2(d^2y)/(dx^2)= (a)n(n-1)y (b) n(n+1...

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  20. If x=t^2,\ \ y=t^3 , then (d^2y)/(dx^2)= (a)3//2 (b) 3//4t (c) 3//2t ...

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