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Reduce the equation y^3dy+(x+y^2)dx=0 to...

Reduce the equation `y^3dy+(x+y^2)dx=0` to a homogeneous equation and then solve it.

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The correct Answer is:
`1/2 ln |x^2 +a^2| -tan^-1 (a/x) = c, where a = x+y^2`
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MOTION-DIFFERENTIAL EQUATION -Exercise 3
  1. Solve: xdy+ydx= (xdy-ydx)/(x^(2)+y^(2))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Find the curve y= f(x) where f(X) ge 0, f(0) =0,bounding a curvilinear...

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  20. Find the equation of a curve such that the projection of its ordinate ...

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