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For the differential equations, find a p...

For the differential equations, find a particular solution satisfying given condition;
`(x^(3) + x^(2) + x+ 1)(dy)/(dx) = 2x^(2) + x, y = 1` when x = 0.

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Verified by Experts

The correct Answer is:
`y = (1)/(4) log [ (x + 1)^(2)(x^(2) + 1)^(3)]- (1)/(2) tan^(-1) x+ 1`
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NCERT TAMIL-DIFFERENTIAL EQUATIONS-EXERCISE - 9.4
  1. The solution of sec^(2)x tany dx+sec^(2)y tanx dy=0 is

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  2. For each of the differential equations in (e^(x)+e^(-x))dy-(e^(x)-e^...

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

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  4. Differential equation y log y dx - x dy = 0

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  5. Differential equation x^(5)(dy)/(dx) = - y^(5)

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  6. (dy)/(dx) = sin^(-1)x

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  7. e^(x) tan y dx + (1 - e^(x))sec^(2)y dy = 0

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  8. For the differential equations, find a particular solution satisfying ...

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  9. x(x^(2) - 1)(dy)/(dx) = 1, y = 0 when x = 2.

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  10. cos ((dy)/(dx)) = a (a ne R), y = 2 when x = 0

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  11. (dy)/(dx) = y tan x, y = 1 when x = 0

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  12. Find the equation of a curve passing through the point (0,0) and whose...

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  13. For the differential equation xy(dy)/(dx) = (x + 2)( y + 2), find the ...

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  14. Find the equation of a curve passing through the point (0,-2). Given t...

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  15. At any point (x,y) of a curve, the slope of the tangent is twice the s...

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  16. The volume of spherical balloon being inflated changes at a constant r...

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  17. In a bank, principal increases continuously at the rate of r% per year...

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  18. In a bank, principal increases continuously at the rate of 5% per year...

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  19. In a culture, the bacteria count is 1,00,000. The number is increased ...

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  20. The general solution of the differential equation (dy)/(dx) = e^(x + y...

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