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Which of the following differential eq...

Which of the following differential equations has y = x as one of its particular solution?
(A) `(d^2y)/(dx^2)-x^2(dy)/(dx)+x y=x`
(B) `(d^2y)/(dx^2)+x(dy)/(dx)+x y=x`
(C) `(d^2y)/(dx^2)-x^2(dy)/(dx)+x y=0`
(D) `(d^2y)/(dx^2)+x(dy)/(dx)+x y=0 `

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

Verified by Experts

The correct Answer is:
B
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AAKASH INSTITUTE ENGLISH-DIFFERENTIAL EQUATIONS-Assignment (Section - A) Competition Level Questions
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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 it...

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

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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 a general solution of (d^(2)y)/(dx^(2))-2(dy...

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  7. The solution of 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. The integrating factor of (xdy)/(dx)-y=x^(4)-3x " is"

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

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

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

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  14. The number of solutions of (dy)/(dx)=(y+1)/(x-1),"Then 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)"...

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

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

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