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If y = y(x) is the solution of the diffe...

If y = y(x) is the solution of the differential equation, `x dy/dx+2y=x^2` satisfying y(1) = 1, then `y(1/2)` is equal to

A

`4/64`

B

`13/16`

C

`49/16`

D

`1/4`

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • The solution of the differential equation (dy)/(dx)=e^(x-y)+1 is -

    A
    `e^(y-x)=y+c`
    B
    `e^(x-y)=y+c`
    C
    `e^(x-y)=x+c`
    D
    `e^(y-x)=x+c`

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

    A
    `|(2x-1)/(2y+3)|=c`
    B
    `|(2y+1)/(2x-3)|=c`
    C
    `|(2x-1)/(2y-1)|=c`
    D
    `|(2x+3)/(2y-1)|=c`

  • The solution of the differential equation y dx+(x+x^(2)y)dy=0 is -

    A
    `(1)/(xy)+log|y|=c`
    B
    `-(1)/(xy)+log|y|=c`
    C
    `(1)/(xy)+2log|y|=c`
    D
    `log|y|=cx`

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