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Find the particular solution of the following differential equation: `(dy)/(dx)=1+x^2+y^2+x^2y^2,` given that `y=1\ ` when `x=0.`

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The correct Answer is:
`tan^(-1)y=x+1/3 x^(3)+pi/4`
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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-EXERCISE 9 (f) Long Answer Type Questions (I)
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  5. Find the particular solution of the following differential equation...

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  6. Find the particular solution of the following : (dy)/(dx)= 4 xy^(2),...

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  7. Find the particular solution of the following : (dy)/(dx)= y tan x, ...

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  8. Find the particular solution of the differential equation e^xsqrt(1-y^...

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  9. Find the particular solution of the following : (x+1)(dy)/(dx)=2e^(-...

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  10. Find the particular solution of the following : sec^(2)x tan y dx - ...

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  11. Find the particular solution of the following : (dy)/(dx)=x^(3) cose...

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  12. Find the particular solution of the following : (dy)/(dx)= (x(2 log ...

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  13. Find the particular solution of : (i) log(dy/dx)=2x+y (ii) log(d...

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  14. The normal lines to a given curve at each point pass through (2,0). Th...

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

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  16. Find the particular solution of the differential equation xy(dy)/(d...

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  17. In a bank, principal increases continuously at the rate of 5% per y...

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

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  19. A population grows at the rate of 8% per year. How long does it tak...

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  20. The surface area of a balloon, being inflated, changes at a rate propo...

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