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

\(\sin \left( {\frac{{\pi x}}{2}} \right)\)

\({e^x}\sin \left( {\frac{{\pi x}}{2}} \right)\)

\({e^{ - x}}\sin \left( {\frac{{\pi x}}{2}} \right)\)

Consider the differential equation \({x^2}\frac{{{d^2}y}}{{d{x^2}}} +

1.	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
A.	x2
B.	\(\sin \left( {\frac{{\pi x}}{2}} \right)\)
C.	\({e^x}\sin \left( {\frac{{\pi x}}{2}} \right)\)
D.	\({e^{ - x}}\sin \left( {\frac{{\pi x}}{2}} \right)\)
Answer» B. \(\sin \left( {\frac{{\pi x}}{2}} \right)\)

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