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Solve the differential equation (1+x^(2)...

Solve the differential equation `(1+x^(2))(dy)/(dx)=x`.

A

`y=tan^(-1) x +c `

B

`y=-tan^(-1) x +c `

C

`y=1/2 log_e(1+x^2)+c `

D

`y=-1/2 log_e (1+x^2) + c `

Text Solution

Verified by Experts

The correct Answer is:
C
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TARGET PUBLICATION-DIFFERENTIAL EQUATIONS -EVALUATION TEST
  1. Solve the differential equation (1+x^(2))(dy)/(dx)=x.

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  2. The order of the differential equation satisfying sqrt(1-x^4)+sqrt(1-y...

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  3. The degree of the differential equation (d^3y)/(dx^3)+x((dy)/(dx))^4 =...

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  4. The equation of the curve in which the portion of the tangent included...

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  5. The degree of the differential equation satisfying the relation sqrt(1...

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  6. The solution of the differential equation (dy)/(dx)=y/x+(f(y/x))/((f')...

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  7. The solution of (dy)/(dx)+yf'(x)-f(x).f'(x)=0,y!=f(x) is

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  8. A function y=f(x) satisfies (x+1)f^(prime)(x)-2(x^2+x)f(x)=(e^x^2)/((x...

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  9. The solution of dy/dx = (x^2+y^2+1)/(2xy) satisfying y(1)=0 is given b...

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  10. The solution of the differential equation xdx+ydy+(xdy-ydx)/(x^(2)+y^(...

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  11. The solution of the differential equation 2x^2y"dy"/"dx"=tan(x^2y^2) ...

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  12. The solution of the differential equation x^(3)(dy)/(dx)+4x^(2) tany=e...

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  13. The general solution of the differential equation (dy)/(dx) = y tan x ...

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  14. The equation of the curve satisfying the eqution (xy=x^(2)) (dy)/(dx)...

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  15. Solution of the equation (dy)/(dx)=e^(x-y)(1-e^y) is

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  16. The x-intercept of the tangent to a curve is equal to the ordinate of ...

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  17. The differential equation (dy)/(dx)=sqrt(1-y^(2))/(y) determines a fam...

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  18. Which one of the following functions is not homogeneous ?

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  19. A curve passes through (1,pi/4) and at (x,y) its slope is (sin 2y)/(x+...

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  20. The equation of the family of curves which intersect the hyperbola xy-...

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  21. Find the equation of a curve passing through (0,1) and having gradient...

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