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Solve the following differential equatio...

Solve the following differential equations:
`(xy^2+x)dx+(yx^2+y)dy=0`

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`(x^2+1)(y^2+1)=c`
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PATHFINDER-BASIC MATHEMATICS-QUESTION BANK
  1. Evaluate : int0^1(x^5)/(1+x^12)dx

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  2. Evaluate : int0^(pi//2) cos^3xcdot sinx dx

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  3. Solve the following differential equations: (xy^2+x)dx+(yx^2+y)dy=0

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  4. Solve the following differential equations: dy/dx=e^(x+y)+x^2 e^y

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  5. The value of lim(nrarrprop) ((n+1)(2n+1))/n^2 is

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  6. The derivative of sqrt((e^(sqrtx))) with respect to x is

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  7. If ysqrt(1-x^2)+xsqrt(1-y^2)=1 when |x|lt1 and |y|lt1 find dy/dx

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  8. The angle between the tangents to the curves y=sin x and y = cos x at ...

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  9. The maximum value of (1/x)^x, xgt0 is

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  10. If y=tan^-1((sqrt(1+x^2)-1)/x), then dy/dx at x = 0 is

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  11. The slope of the tangent to the curve xy=c^2 at (ct,c/t)is

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  12. int dx/(x+sqrtx) is equal to

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  13. The value of int-2^3sqrt(x^2-2x+1 dx is

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  14. The solution of the differential equation ysqrt(1+x^2) dy+xsqrt(1+y^...

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  15. The value of 'a' for which the function f(x)= sinx-cosx-ax+b decreases...

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  16. If f(x)=abs(sinx)+abs(cosx),then int0^pi f(x) dx is equal to

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  17. A particle moves along a straight line according to the law s=t^3/3 -3...

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  18. number of solution of the integral part of {1+x}+2x=4[x+1]-6 is

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  19. Solution set of x satisfying (x)^2=[x]^2+2x is where [x] and (x) are t...

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  20. Number of solution of equation [x]^2=x+2{x} is/are , where [.] and {.}...

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