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Findy2 in each of the following cases: ...

Find`y_2` in each of the following cases:
`x=acos^3theta`,`y=asin^3theta`

Text Solution

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The correct Answer is:
`1/(3asinthetacos^4theta)`
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CHHAYA PUBLICATION-SECOND ORDER DERIVATIVE-Short Answer type Question
  1. Find (d^2y)/(dx^2) when: sinx+cosy=1

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  2. Find (d^2y)/(dx^2) when: x^py^q=(x+y)^(p+q)

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  3. Findy2 in each of the following cases: x=acos^3theta,y=asin^3theta

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  4. Findy2 in each of the following cases: x=a(theta+sintheta),y=a(1-cost...

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  5. Findy2 in each of the following cases: x=a(t+1/t),y=a(t-1/t)

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  6. Findy2 in each of the following cases: x=e^t,y=sint at t=pi/2

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  7. Findy2 in each of the following cases: x=a(costheta+thetasintheta),y=...

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  8. Findy2 in each of the following cases: sinx=(2tantheta)/(1+tan^2theta...

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  9. Find y2 in each of the following cases: y=t^2+t^3,x=t-t^4

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  10. IF y^3=x^2+y^2, find (d^2y)/(dx^2) at y=1.

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  11. IF y=x/(x^2-x-2), find the value of y2 at x=1.

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  12. IF y=xsinx, prove that, x^2(d^2y)/(dx^2)-2xdy/dx+(2+x^2)y=0

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  13. If y=ae^(mx)+bcosmx, prove that, (d^2y)/(dx^2)+m^2y=2am^2e^(mx)

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  14. IF y=e^(-x)(cosx+sinx), show that ,y2+2y1+2y=0.

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

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  16. If y=x^3log""1/x, Prove that , xy2-2y1+3x^2=0.

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  17. If y=log(x+sqrt(x^2+a^2)), show that (a^2+x^2)y2+xy1=0

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  18. If y=[log(x+sqrt(x^2+1))]^2, show that, (1+x^2)(d^2y)/(dx^2)+xdy/dx=...

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  19. IF y=secx+tanx, show that , y2-yy1=0.

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  20. If y=3cos(logx)+4sin(logx), Prove that x^2y2+xy1+y=0

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