Consider the differential equation \({x^2}\frac{{{d^2}y}}{{d{x^2}}} + x\frac{{dy}}{{dx}} - 4y = 0\) with the boundary conditions of y(0) = 0 and y(1) = 1. The complete solution of the differential equation is
1
x2
2
\(\sin \left( {\frac{{\pi x}}{2}} \right)\)
3
\({e^x}\sin \left( {\frac{{\pi x}}{2}} \right)\)
4
\({e^{ - x}}\sin \left( {\frac{{\pi x}}{2}} \right)\)