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Find the equation of a curve passing thr...

Find the equation of a curve passing through the origin, given that the slope of the tangent of the curve at any point `(x,y)` is equal to tha sum of the coordinates of the point.

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The correct Answer is:
`x + y + 1= e^(x)`
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NCERT TAMIL-DIFFERENTIAL EQUATIONS-EXERCISE - 9.6
  1. Find the general solution : .(dy)/(dx) + 2y = sin x

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  2. (dy)/(dx) + 3y = e^(-2x)

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  3. solve each of the differential equations given in (dy)/(dx)+(y)/(x)=...

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  4. For each of the differential equations given in (dy)/(dx)+secx.y=tan...

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  5. cos^(2)x(dy)/(dx) + y = tan x (o le x le (pi)/(2))

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  6. For each of the differential equations given in x(dy)/(dx)+2y=x^(2)l...

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  7. x log x(dy)/(dx) + y = (2)/(x)log x

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  8. (1 + x^(2))dy + 2xy dx = cot x dx (x ne 0)

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  9. Find a particular solution of the differential equation (dy)/(dx) + y...

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  10. For each of the differential equations given in (x+y)(dy)/(dx)=1

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

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  12. (x + 3y^(2))(dy)/(dx) = y ( y rt 0).

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  13. For each of the differential equations given in find a particular solu...

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  14. For each of the differential equations given in find a particular solu...

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  15. (dy)/(dx) = 3y cot x = sin 2x, y = 2 when x = (pi)/(2)

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  16. Find the equation of a curve passing through the origin, given that th...

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  17. Find the equation of a curve passing through the point (0,2), given th...

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  18. The integrating factor of the fifferential equation x(dy)/(dx)-y=2x^(2...

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  19. The integrating factor of the fifferential equation (1-y^(2))(dy)/(dx)...

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