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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

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The correct Answer is:
7
`(dy)/(dx)+(2/x)y=x`
I.F.`e^(int 2/x dx)=x^(2)impliesyx^(2)=intx xx x^(2) dximpliesyx^(2)=(x^(4))/4+c`
`y(1)=1impliesc=3/4`
Hence `y=1/(4x^(2))(x^(4)+3)impliesy(1/2)=49/16`
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