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The solution of (dy)/(dx)+y=e^(-x),y(0)=...

The solution of `(dy)/(dx)+y=e^(-x),y(0)=0`, is

A

`y = e^(-x)(x-1)`

B

`y = xe^(x)`

C

`y = xe^(-x) + 1`

D

`y = xe^(-x)`

Text Solution

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The correct Answer is:
D
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AAKASH INSTITUTE-DIFFERENTIAL EQUATIONS-Assignment (Section - A) Competition Level Questions
  1. Which of the following differential equations has y = x as one of its...

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  2. The differential equation for which y=a cos x+b sin x is a solution, ...

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  3. The solution of (dy)/(dx)+y=e^(-x),y(0)=0, is

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  4. Which of the following is general solution of (d^(2)y)/(dx^(2)) - 2(dy...

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  5. Solution of the differential equation xdy-ydx=0 represents

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  6. Integrating factor of differential equation cosx(dy)/(dx)+ysinx=1 is (...

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  7. Solution of the differential equation tan y.sec^(2) x dx + tan x. sec^...

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  8. Integrating factor of x(dy)/(dx) - y = x^(4) - 3x is

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  9. The general solution of differential equation (e^(x) + 1) y dy = (y + ...

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

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  11. The solution of differential equation (dy)/(dx) + (2xy)/(1+x^(2)) = (1...

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  12. The number of solution of dy / dx = (y +1) / (x-1) when y(1) = 2 is

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  13. The differential equation y(dy)/(dx) + x = c represents

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  14. The integrating factor of differential equation dy/dx+y=(1+y)/x is

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  15. The differential equation for the family of curves x^(2)-y^(2)-2ay=0, ...

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  16. The general solution of (dy)/(dx) = 2x e^(x^(2)-y) is

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  17. The curve in which the slope of the tangent at any point equal the rat...

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  18. The solution of the equation (2y-1)dx - (2x + 3)dy = 0 is

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  19. Let f(x) = secx*f'(x), f(0) = 1, then f(pi/6) is equal to (i)1/sqrte ...

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  20. The integrating factor of (1+y^(2)) dx = (tan^(-1)y-x) dy is -

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