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Find the general solution of the differe...

Find the general solution of the differential equation `x(dy)/(dx)+ 2y= x^(2) (x ne 0)`

A

`y = (x^(2)+c)/(4x^(2))`

B

`y = x^(2)/4 + c`

C

`y = (x^(4)+c)/(x^(2))`

D

`y = (x^(4)+c)/(4x^(2))`

Text Solution

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The correct Answer is:
D
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HIMALAYA PUBLICATION-DIFFERENTIAL EQUATIONS-QUESTION BANK
  1. Which of the following is not a homogeneous function of x and y

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  2. Solution of the differential equation (dx)/(x)+(dy)/(y)=0 is

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  3. Find the general solution of the differential equation x(dy)/(dx)+ 2y=...

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  4. The degree of the differential equation ((d^(2)y)/dx^(2))^(2)+(dy/dx)^...

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  5. The degree of the equation [1+(dy/dx)^(2)]^(3/2) = ((d^(2)y)/dx^(2)) i...

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  6. The order and degree of the differential equation (d^(2)y)/dx^(2) + (d...

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  7. If y=e^(-x)(Acosx+Bsinx), then y satisfies :

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  8. The differential equation for y = A cos alpha x + B sin alpha x Where ...

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

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  10. Integrating factor of the differential equation cos x dy/dx + y sin x ...

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  11. The solution of the differential equation y sec^(2) x dx + tan x . Sec...

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  12. The family y=ax+a^3 of curves is represented by the differential equat...

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

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  14. Solution of dy/dx-y =1, y(0) =1 is given by

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

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  16. Which of the following is a second order differential equation?

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  17. Integrating factor of the differential equation (1-x^(2)) dy/dx- xy =1...

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  18. tan^(-1)x+tan^(-1)y = c is the general solution of the differential eq...

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

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  20. The general solution of e^x cos y dx - e^x sin y dy = 0 is :

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