MAT244--2018F > Quiz-3

Q3 TUT 5102

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Victor Ivrii:
Find the Wronskian of two solutions of the given differential equation without solving the equation.
$$x^2y''+xy'+(x^2-\nu^2)y=0 \qquad\text{Bessel's equation}.$$

Yiting Zhang:
$$y'' + \frac{x}{x^2}y' + \frac{x^2-v^2}{x^2}y = 0$$
$$W = ce^{-\int p(t)dt}$$
$$p(t) = \frac{1}{x}$$
$$-\int p(t)dt = -\ln{x}$$
$$W = ce^{-\ln{x}} = ce^{\ln{\frac{1}{x}}} = \frac{c}{x}$$

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