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GATE ME 2012 | Question: 46

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Consider the differential equation $x^2 \dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}-4y=0$ with the boundary conditions of $y(0)=0$ and $y(1)=1$. The complete solution of the differential equation is

  1. $x^2 \\$
  2. $\sin \left (\dfrac{\pi x}{2} \right ) \\$
  3. $e^x \sin \left (\dfrac{\pi x}{2} \right ) \\$
  4. $e^{-x} \sin \left (\dfrac{\pi x}{2} \right) \\$
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