Discussion
The Cauchy-Euler equation \( x^{2}y'' + axy' + by = 0 \) is solved by trying
Answer: B
Each term then carries the same power of \( x \), since \( x^{2} \) times the second derivative of \( x^{m} \) is \( m(m-1)x^{m} \), and the equation collapses to an algebraic one in \( m \). The exponential trial belongs to the constant-coefficient case, where it is the derivatives rather than the coefficients that carry the variable
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