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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

  • If y=y(x) is the solution of the differential equation xdy/dx+2y=x^2 satisfying y(1)=1, then y(1/2) is equals to

    A
    `7/64`
    B
    `1/4`
    C
    `49/16`
    D
    `13/16`

  • The solution of the differential equation y(dy)/(dx)=x-1 satisfying y(1) = 1, is

    A
    `y^(2)=x^(2)-2x+2`
    B
    `y^(2)=2x^(2)-x-1`
    C
    `y=x^(2)-2x+2`
    D
    none of these

  • The solution of the differential equation (dy)/(dx)=1/(x+y^2) is

    A
    `y=-x^2-2x-2+Ce^x`
    B
    `y=x^2+2x+2-Ce^x`
    C
    `x=-y^2-2y+2-Ce^y`
    D
    `x=-y^2-2y-2+Ce^y`

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    Explore conceptually related problems

    If y = y(x) is the solution of the differential equation, x (dy)/(dx) + 5y = 10x^5, x > 0 satisfying y(1) = 2 then range of y(x) for x > 0 is:

    The solution of the differential equation dy/dx = (1+x)(1+ y^2) is -

    The solution of the differential equation (dy)/(dx) = 1/(x+y^(2)) is

    The solution of the differential equation (dy)/(dx)=(4x+y+1)^(2) , is

    The solution of the differential equation x(dy)/(dx) + 2y = x^2 (X ne 0) with y(1) =1, is :

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