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

If `x=sin theta,y=cosptheta,p rov e \ t h a t` `(1-x^2)y_2-x y_1+p^2y=0,w h e r e \ y_2=(d^2y)/(dx^2) \ a n d \ y_1=(dy)/(dx)`

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If x=sintheta , y=cosptheta , prove that (1-x^2)y_2-x y_1+p^2y=0 , where y_2=(d^2y)/(dx^2) and y_1=(dy)/(dx) .

If x=sint,y=sinpt , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2 y=0 .

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If x=sint ,y=sinpt , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y=0.

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If e^y(x+1)=1,s howt h a t(d^2y)/(dx^2)=((dy)/(dx))^2dot

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If y=sqrt((1-x)/(1+x)),p rov et h a t(1-x^2)(dy)/(dx)+y=0

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RD SHARMA ENGLISH-HIGHER ORDER DERIVATIVES-All Questions
  1. If y=2 sin x+3cos x, show that (d^2y)/(dx^2)+y=0

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

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

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

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  6. If y^3-y=2x ,p rov et h a t(d^2y)/(dx^2)=(-24 y)/((3y^2-1)^3)

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  7. If y=x^x ,f i n d \ (d^2y)/(dx^2)

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  8. If y=sin^(-1)x , \ s how \ t h a t \ (d^2y)/(dx^2)=x/((1-x^2)^(3/2))

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  9. If y=Acosn x+Bsinn x ,s howt h a t (d^2y)/(dx^2)+n^2y=0

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  10. If y=tanx+secx ,p rov e \ t h a t \ (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

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  11. If y=(a x+b)/(x^2+c), then (2x y1+y) y3=

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  12. If y=(log)e(x/a)^x ,then x^3y2= (a) (xy1-y)^2 (b) ((y-x y1)/(y1))^2 ...

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  13. If sin^-1x + sin^-1(1-x) = sin^-1sqrt[1-x^2],then x is equal to

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  14. If y=2/(sqrt(a^2-b^2))tan^(-1){sqrt((a-b)/(a+b))tan(x/2)} , then show ...

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  15. If y=x^(n-1)lnx then x^2y2+(3-2n)x y1 is equal to (a) -(n-1)^2y (b) (...

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  16. If x y-(log)e y=1 satisfies the equation x(y y2+y1 2)-y2+lambday y1=0,...

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  17. If x=f(t )cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost ,t h ...

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  18. If d/(dx){x^n-a1x^(n-1)+a2x^(n-2)++(-1)^n an}e^x=x^n e^x , then the va...

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  19. If x=f(t) and y=g(t), then (d^2y)/(dx^2) is equal to

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  20. Let f(x) be a polynomial.Then, the second order derivative of f(e^x) ...

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