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In the parabola y^2=4ax, prove that (d^2...

In the parabola `y^2=4ax`, prove that `(d^2y)/(dx^2).(d^2x)/(dy^2)=(-2a)/y^3`

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CHHAYA PUBLICATION-SECOND ORDER DERIVATIVE-Long answer type Question
  1. IF y=(cos^-1x)^2, prove that,(1-x^2)(d^2y)/(dx^2)-xdy/dx-2=0. Hence,...

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  2. If y=e^x, Prove that , xy2-(2x-1)y1+(x-1)y=0.

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  3. In the parabola y^2=4ax, prove that (d^2y)/(dx^2).(d^2x)/(dy^2)=(-2a)/...

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  4. If x=cos t and y=log t , prove that at t=pi/2, (d^2y)/(dx^2)+(dy/dx)^2...

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  5. IF x=t^2+2t,y=t^3-3t, where t is a parameter then show that, (d^2y)/(d...

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  6. If y=ae^(tsqrt2)+be^(-tsqrt2) and x= sin t, show that, (1-x^2)(d^2y)...

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  7. Evaluate int sin3x sin5xdx.

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  8. If x=1/z and y=f(x), then prove that, (d^2f)/(dx^2)=2z^3dy/dz+z^4(d^...

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  9. Putting logx=z show that, x^2(d^2y)/(dx^2)=(d^2y)/(dz^2)-dy/dz.

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  10. If x=Ae^(-(kt)/2)cos(pt+in), and A,k,p,in are constants, show that (d^...

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  11. IF y^4+5xy+y=2, find dy/dxand(d^2y)/(dx^2), when x=0,y=1.

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  12. If F(x) =f(x)phi(x) and f'(x)phi'(x)=a (a constant), then prove that ,...

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  13. IF y=e^(ax)sin bx, then prove that, (d^2y)/(dx^2)-2ady/dx+(a^2+b^2)...

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  14. If y=cosecx+cotx, then show that,(d^2y)/(dx^2)=sinx/(1-cosx)^2.

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  15. IF y^2=ax^2+2bx+c, Prove that (d^2x)/(dy^2)=(b^2-ac)/(ax+b)^3.

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  16. IF y=Ae^(mx)+Be^(nx), show that y2-(m+n)y1+mny=0.

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  17. IF xsqrt(1+y)+ysqrt(1+x)=0, show that, dy/dx=-1/(1+x)^2

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  18. IF xsqrt(1+y)+ysqrt(1+x)=0, show that, (d^2y)/(dx^2)=2/(1+x)^3.

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  19. IF y=e^(msin^-1x), find the value of (y2)0.

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  20. IF y=sqrt(sin x+sqrt(sin x +sqrt(sin x +.... oo), show that (2y-1)^3...

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