# given y=1/x is a solution 2x^2 d2y/dx + xdy/dx - 3y = 0 , x>0 a) Find a linearly independent solution by reduction the order approach b) Show that 2 solutions are linearly independent c) Write a general solution

Question
Applications of integrals
given $$\displaystyle{y}=\frac{{1}}{{x}}$$ is a solution $$\displaystyle{2}{x}^{{2}}{d}{2}\frac{{y}}{{\left.{d}{x}\right.}}+{x}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}-{3}{y}={0},{x}{>}{0}$$
a) Find a linearly independent solution by reduction the order approach
b) Show that 2 solutions are linearly independent
c) Write a general solution

2021-02-27

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