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Solve: xdy+ydx= (xdy-ydx)/(x^(2)+y^(2)...

Solve:
`xdy+ydx= (xdy-ydx)/(x^(2)+y^(2))`

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Verified by Experts

The correct Answer is:
`xy + tan^-1 y/x =c`
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MOTION-DIFFERENTIAL EQUATION -Exercise 3
  1. dy/dx =(y)/(2y^3+x)

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  2. Solve ((dy)/(dx))=e^(x-y)(e^x-e^y)dot

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  3. Solve: xdy+ydx= (xdy-ydx)/(x^(2)+y^(2))

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  4. (a)dy/dx = (xy)/(x^2+y^2)

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  5. Reduce the equation y^3dy+(x+y^2)dx=0 to a homogeneous equation and th...

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  6. Solve : {xcos(y/x)+ysin(y/x)}ydx={ysin(y/x)-xcos(y/x)}xdy

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  7. Solve (x-y)dy=(x+y+1)dx

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  8. (dy)/(dx)=(x+y+1)/(2x+2y+3)

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  9. Show that the curve such that the distance between the origin and the ...

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  10. Let f(x, y, c1) = 0 and f(x, y, c2) = 0 define two integral curves of ...

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  11. Let y=y(t) be a solution to the differential equation y^(prime)+2t ...

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  12. Solution of the differential equation (1-x^(2))(dy)/(dx)+2xy=xsqrt(1-x...

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

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  14. dy/dx -yln2 = 2^sinx. (cosx-1) ln 2, y being bounded when x rightarrow...

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  15. Consider the differential equation. Dy/dx +P(x)y = Q(x) (i) If two par...

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  16. x(1+y^2)dx-y(1+x^2)dy =0

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  17. Find the integral curve of the differential equation, x(1–x lny). Dy/d...

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  18. A tank consists of 50 litres of fresh water. Two litres of brine each ...

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  19. A normal is drawn at a point P(x , y) of a curve. It meets the x-ax...

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  20. Find the curve for which the sum of the lengths of the tangent and sub...

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