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Solve the following differential equatio...

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

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The correct Answer is:
`y=1/4 x^(2)- x/4 sin2x-1/8 cos 2x+log |log x|+c`.
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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE 9 (d) Short Answer Type Questions
  1. Find the general solution of the following : (x+2)(dy)/(dx)=x^(2)+4...

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  2. Write the general solution of the following differential equations (...

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  3. Find the general solution of the following : sqrt(1-x^(6))dy=x^(2)d...

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  4. Find the general solution of the following : (4+5 sin x)(dy)/(dx)= ...

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  5. Find the general solution of the following : (dy)/(dx)=cos^(3)x sin...

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  6. Find the general solution of the following : (dy)/(dx)= (1)/(sin^(4...

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  7. Find the general solution of the differential equation (dy)/(dx) =si...

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  8. Find the general solution of the following : (1+cos x)(dy)/(dx)= (1...

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  9. Find the general solution of the following : (1+cos x) dy= (1- cos ...

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  10. Find the general solution of the following : (dy)/(dx)= log x.

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

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  12. Find the general solution of the following : (dy)/(dx)+3x= e^(-2x).

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  13. dy / dx = sin^3x cos^2x + x e^x

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  14. Solve : (dy)/(dx)= (1)/(1+x^(2)), y(0)=3.

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  15. (x^3+x^2+x+1)(dy)/(dx)=2x^2+x ; y=1w h e nx=0

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  16. cos((dy)/(dx))=a\ (a in RR); y=1 when\ x=0

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  17. sin((dy)/(dx))=a, when x=0, y=1

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  18. Find the particular solution of cos((dy)/(dx))=a, given that y=2 when ...

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  19. Find the particular solution of e^(dy/dx)=x+1, given that when x=0,y=3...

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  20. Find the equation of the curve passing through the point (1, 1) whose...

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