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If x =sin t,y = sin 2t then prove that `(1-x^2)(d^2y)/(dx^2)- x dy/dx + 4y = 0`

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(i) If x=sin t , y=sin 2t then prove that (1-x^2)d^2y/dx^2-xdy/dx+4y=0 . If y=gof (x) then find dy/dx.

(i) if x=sint , y= sinpt , then show that (1-x^2) d^2 y/dx^2 - x dy/dx +p^2 y =0 . Br Determine the differentials of z=cos 2t -2 cot t .

If x = sint and y= sin (pt) , then show that (1-x^(2) ) (d^2y)/( dx^2) - x (dy)/( dx) + p^(2) y =0 .

If x=cos theta and y=sin 5 theta , then prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+25y=0

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If y=e^(x)sinx , then prove that (d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0 ,

if x=e^(t)sin t and y=e^(t)cos t , then prove that (x+y)^(2)(d^(2)y)/dx^(2)=2(xdy/dx-y) .

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MODERN PUBLICATION-TEST PAPER 5-PROBLEM
  1. Determine the interval in which the function f(x) = x^3-5x^2+3x+97 is ...

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  2. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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  3. Evaluate int0^2abs(x^2+2x-3)dx

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  4. solve:ydx-xdy=xydx

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  5. int(xe^x)/(1+x^2)dx

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  6. int0^pi(xdx)/(1+sinx)

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  7. Solve : (x + 2y^3)dy/dx = y.

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  8. If the position vectors of the points A, B, C are 2hat(i) + hat(j) - h...

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  9. Find the foot of the perpendicular drawn from the point (5,7,3) to the...

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  10. Passing throughthe point (2,-3,1) and (-1,1-7) and perpendicular to th...

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  11. Find the direction cosines of the line which is perpendicular to the l...

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  12. Show that the shrtest distance of the point (0, 8a) from the curve ax^...

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  13. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

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  14. Exaniming consistency and solvability, solve the following equations b...

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  15. Prove the following: |[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],...

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  16. If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx +...

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  17. Show that the semi-vertical angle of a right circular cone of minimum ...

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  18. int0 ^pi (( tan x) / (sinx +tan x))dx

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  19. Find the area of the regions into which the circle x^2+y^2=4 is divide...

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  20. Find the distance of the point (1,-1,-10) from the line (x-4)/1=(y+3)/...

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