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The elimination of the arbitrary constan...

The elimination of the arbitrary constant k from the equation `y=(x+k)e^(-x)` gives the differential equation

A

`(dy)/(dx)-y=e^(-x)`

B

`(dy)/(dx)-ye^x = 1 `

C

`(dy)/(dx)+ ye^(x)=1`

D

`(dy)/(dx)+ y =e^(-x)`

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The correct Answer is:
D
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TARGET PUBLICATION-DIFFERENTIAL EQUATIONS -EVALUATION TEST
  1. The elimination of the arbitrary constant k from the equation y=(x+k)e...

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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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