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Find y2 in each of the following cases: ...

Find `y_2` in each of the following cases:
`y=t^2+t^3`,`x=t-t^4`

Text Solution

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The correct Answer is:
`(12t^4+16t^3+6t+2)/(1-4^3)^3`
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CHHAYA PUBLICATION-SECOND ORDER DERIVATIVE-Short Answer type Question
  1. Findy2 in each of the following cases: x=a(costheta+thetasintheta),y=...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. IF y=xsin(logx)+xlogx, Prove that, x^2(d^2y)/(dx^2)-xdy/dx+2y=2xlogx

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  16. IF y=x^2cosx, prove that ,x^2y2-4xy1+(x^2+6)y=0.

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  17. If cosx=ycos(a+x), prove that, (d^2y)/(dx^2)=2sinasec^2(a+x)tan(a+x)

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  18. If y=sin(logx), prove that , x^2y2+xy1+y=0.

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  19. If logy=sin^-1x, show that, (1-x^2)(d^2y)/(dx^2)=xdy/dx+y.

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  20. IF y=cos(cos x), show that, y2-y1cotx+ysin^2x=0.

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