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The solution of differential equation ...

The solution of differential equation
`(1+x^(2)) (dy)/(dx) + y = e^(tan^(-1)x)`

A

`ye^(tan^(-1)x) = (1)/(2)e^(2tan^(-1)x) + C`

B

`y = (1)/(2)e^(2 tan^(-1)x) + C`

C

`ye^(tan^(-1)x) = 2e^(2 tan^(-1)x) + C`

D

`y. tan^(-1) x = (1)/(2) e^(2 tan^(-1)x) + C`

Text Solution

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The correct Answer is:
A
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AAKASH INSTITUTE-DIFFERENTIAL EQUATIONS-Assignment Section - B (Objective Type Questions (One option is correct))
  1. The solution of the differential equation (dy)/(dx) = (y)/(x)+ (Q((...

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  2. The solution of differential equation x^(2)y^(2)dy = (1-xy^(3))dx is

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  3. The solution of differential equation (1+x^(2)) (dy)/(dx) + y = e^(...

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  4. The solution of the differential equation ydx+ (x +x^2 y) dy =0 is

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  5. The family whose x and y intercepts of a tangent at any point are resp...

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  6. The solution of the equation y' = cos (x-y) is

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  7. Solution of y dx - x dy = x^(2)ydx is

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  8. The equation of the curve, slope of whose tangent at any point (h, k) ...

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  9. The second order differential equation is

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  10. The order of the differential equation whose general solution is y = (...

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  11. The real value of n for which substitutor transform differential equat...

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  12. The equation of curve in which portion of y-axis cutoff between origin...

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  13. A curve y = f(x) passes through point P(1,1). The normal to curve at p...

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  14. Solve the following differential equation: tany(dy)/(dx)=sin(x+y)+sin(...

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  15. For solving dy/dx = 4x +y +1, suitable substitution is

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  16. A continuously differentiable function phi(x) in (0,pi) satisfying y'=...

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  17. Solve (1+e^((x)/(y)))dx + e^((x)/(y)) (1-(x)/(y))dy = 0

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  18. Order of the differential equation of the family of all concentric cir...

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  19. The number of solutions of y'=(y+1)/(x-1),y(1)=2 is

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  20. The differential sin^(-1) x + sin^(-1) y = 1, is

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