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Show that the function varphi defined by...

Show that the function `varphi` defined by `varphi(x)=cos x\ (x in RR)` ; satisfies
the initial value problem `(d^2y)/(dx^2)+y=0, y(0)=1,\ y^(prime)(0)=0`.

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RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
  1. For each of the following differential equations verify that the accom...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. Solve the following differential equation: (dy)/(dx)=xlogx

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  18. Solve the following differential equation: (x^3+x^2+x+1)(dy)/(dx)=2x^2...

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  19. Solve the following differential equation: (dy)/(dx)=x^5+x^2-2/x ,\ x!...

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  20. Solve the following differential equation: (x^2+1)(dy)/(dx)=1

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