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Show that y=e^x(A\ cos x+Bsinx) is the s...

Show that `y=e^x(A\ cos x+Bsinx)` is the solution of the differential equation `(d^2y)/(dx^2)-2(dy)/(dx)+2y=0.`

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RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
  1. Show that y=a x^3+b x^2+c is a solution of the differential equation (...

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  2. Show that y=(c-x)/(1+c x) is a solution of the different equation (1+x...

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  3. Show that y=e^x(A\ cos x+Bsinx) is the solution of the differential eq...

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  4. Verify thaty=c x+2c^2 is a solution of the differential equation 2((dy...

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  5. Verify that y=-x-1 is a solution of the differential equation (y...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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