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If y=e^(x)sinx, prove that (D^(2)y)/(dx^...

If `y=e^(x)sinx,` prove that `(D^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0`.

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RS AGGARWAL-DIFFERENTIATION-Exercise 10I
  1. If y=a cos (logx)+b sin (logx), prove that x^(2)y(2)+xy(1)+y=0.

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  2. Find the second derivative of e^(3x)sin4x.

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  3. Find the second derivative of sin 3x cos 5x.

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  4. If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0

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  5. If y=(logx)/x , show that (d^2y)/(dx^2)=(2logx-3)/(x^3) .

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  6. If y=e^(ax)cosb x, Show that (d^2y)/(dx^2)-2a(dy)/(dx)+(a^2+b^2)y=0

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  7. If y=e^acos^((-1)x),-1lt=x<1,s howt h a t (1-x^2)(d^2y)/(dx^2)-x(dy)/...

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  8. If x=a t^2,\ \ y=2\ a t , then (d^2y)/(dx^2)= -1/(t^2) (b) 1/(2\ a t^...

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  9. If x=a (theta-sin theta) and y=a(1-cos theta), find (d^(2)y)/(dx^(2)) ...

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  10. If y=sin(logx) , prove that x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 .

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  11. If y=(sin^(-1)x)/(sqrt(1-x^2)) , show that (1-x^2)(d^2y)/(dx^2)-3x(dy)...

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  12. If y=e^(x)sinx, prove that (D^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0.

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  13. If x=a(costheta+log(tan(theta/2)) and y=asintheta then find the value ...

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  14. If x=cost+logtant/2,\ \ y=sint , then find the value of (d^2y)/(dt^2) ...

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  15. If y=x^x , prove that (d^2y)/(dx^2)-1/y((dy)/(dx))^2-y/x=0

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  16. If y=(cot^(-1)x)^(2), then show that (x^(2)+1)^(2)(d^(2)y)/(dx^(2))+2x...

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  17. If y={x +sqrt(x^(2)+1)}^(m), then show that (x^(2)+1)(d^(2)y)/(dx^(2))...

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  18. If y=log{x+sqrt(x^2+a^2)} , prove that: (x^2+a^2)(d^2y)/(dx^2)+x(dy)/(...

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  19. If x=a(costheta+thetasintheta) , y=a(sintheta-thetacostheta) , prove t...

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  20. x=acostheta+bsintheta and y=asintheta-bcostheta, show that y^2(d^2y)/(...

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