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

Question ID - 157484 | SaraNextGen Top Answer

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