The function solves x^2y'' - 3xy' + 4y = 0

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Ordinary differential equations · Ordinary differential equations

Mathematical Methods for Physics, Ch Higher-order linear equations, the Wronskian and variation of parameters

Problem

The function y1=x2y_1 = x^2 solves x2y′′−3xy′+4y=0,x>0.x^2y'' - 3xy' + 4y = 0, \qquad x \gt 0. (a) Check by substitution that y1=x2y_1 = x^2 is a solution. (b) Use reduction of order to find a second solution y2y_2. (c) Compute W(y1,y2)W(y_1, y_2) directly, and confirm that it varies with xx as Abel's identity predicts.

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