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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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To solve the problem, we need to find constants \( A \) and \( B \) such that the function \( y = A \sin(3x) + B \cos(3x) \) satisfies the differential equation: \[ \frac{d^2y}{dx^2} + 4\frac{dy}{dx} + 3y = 10 \cos(3x) \] ### Step 1: Calculate the first derivative \( \frac{dy}{dx} \) ...
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RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If y=e^xcosx , prove that (d^2y)/(dx^2)=2\ e^xcos(x+pi/2) .

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  2. If x=cos t + (log tant)/2, y=sin t, then find the value of (d^2y)/(dt^...

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  3. Find A and B so that y=Asin3x+bcos3x satisfies the equation (d^2y)/(d...

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  4. If x=asint-bcost ,y=acost+bsint ,"p r o v et h a t" (d^2y)/(dx^2)=-...

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  5. If y=e^(ex) (ax+b), show that y^2-4y1+4y=0

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  6. If x=asectheta,y=btantheta,"prove that"(d^2y)/(dx^2)=-(b^4)/(a^2y^3)

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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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  8. If y=(sin^(-1)x)^2 ,prove that (1-x^2)y2-x y1-2=0.

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  9. If y={"log"(x+sqrt(x^2+1))}^2,"show that"(1+x^2)(d^2y)/(dx^2)+x(dy)/(...

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  10. If x=sin(1/alogy),"show that"(1-x^2)y2-xy1-a^2y=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^-x sin x

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

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  14. If y=x^3logx ,"prove that"(d^4y)/(dx^4)=6/xdot

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  15. If y=(logx)/x ,show\ tha 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 t.

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  18. If x=sin theta,y=cosptheta,p rov e \ t 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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