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Verify that y=e^(m cos^-1 x) satisfies t...

Verify that `y=e^(m cos^-1 x)` satisfies the differential equation `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2y=0`

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RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
  1. Verify that y=-x-1 is a solution of the differential equation (y...

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  2. Verity that y^2=4a\ (x+a) is a solution of the differential equatio...

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  3. Verify that y=e^(m cos^-1 x) satisfies the differential equation (1-x...

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  4. Show that the differential equation of which y=2(x^2-1)+c e^-x^2 is a ...

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  5. Verify the solution problems: Show that y = e^-x + ax +b is solution o...

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  6. For each of the following differential equations verify that the accom...

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  7. Verify that the function defined by y = sinx - cosx is a solution of ...

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  8. Show that the function varphi defined by varphi(x)=cos x\ (x in RR) ; ...

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  9. For each of the following initial value problems verify that the accom...

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  10. Solve: (dy)/(dx)=x/(x^2+1)

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  11. Solve: (e^x+e^(-x))dy/(dx)=(e^x-e^(-x))

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  12. Solve the following differential equation: (dy)/(dx)=x^2+x-1/x ,\ x!=0

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  13. Solve the following differential equation: (dy)/(dx)+2x=e^(3x)

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  14. Solve the following differential equation: (dy)/(dx)=(1-cos x)/(1+cosx...

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  15. Solve the following differential equation: (dy)/(dx)=tan^(-1)x

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  16. Solve the following differential equation: 1/x(dy)/(dx)=tan^(-1)x ,\ x...

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  17. Solve the following differential equation: (sinx+cos x)dy+(cos x-sinx)...

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  18. Solve the following differential equation: (dy)/(dx)-xsin^2x=1/(xlogx)

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  19. Solve the following differential equation: sin^4x(dy)/(dx)=cosx

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  20. Solve the following differential equation: sqrt(1-x^4)dy=x\ dx

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