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Which of the following differential equ...

Which of the following differential equations has y = x as one of its particular solution?

A

`(d^(2)y)/(dx^(2)) - x^(2)(dy)/(dx) + xy = x`

B

`(d^(2)y)/(dx^(2)) - x^(2)(dy)/(dx) + xy = 0`

C

`(d^(2)y)/(dx^(2)) + x^(2)(dy)/(dx) + xy = x`

D

`(d^(2)y)/(dx^(2)) + x(dy)/(dx) + xy = 0`

Text Solution

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The correct Answer is:
B
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AAKASH INSTITUTE-DIFFERENTIAL EQUATIONS-Assignment (Section - A) Competition Level Questions
  1. The degree of the differential equation of the curve (x-a)^(2) + y^(2)...

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  2. If y = A sin (theta + B), where A and B are arbitrary constant then to...

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  3. Which of the following differential equations has y = x as one of its...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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