engineering recuitment GATE ECE 2023-24 Test Series Engineering Mathematics Differential Equations Exact Differential Equations
Let y(x) be the solution of the differential equation \({\begin{array}{*{20}{c}} {\frac{d}{{dx}}\left( {x\frac{{dy}}{{dx}}} \right) = x;}&{y\left( 1 \right) = 0,\left. {\frac{{dy}}{{dx}}} \right|} \end{array}_{x = 1}} = 0\) then y(2) is
1
\(\frac{3}{4} + \frac{1}{2}\ln 2\)
2
\(\frac{3}{4} - \frac{1}{2}\ln 2\)
3
\(\frac{3}{4} + \ln 2\)
4
\(\frac{3}{4} - \ln 2\)