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(Solved): Use a CAS to approximate the first four eigenvalues \( \lambda_{1}, \lambda_{ ...



Use a CAS to approximate the first four eigenvalues \( \lambda_{1}, \lambda_{2}, \lambda_{3} \), and \( \lambda_{4} \).
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Use a CAS to approximate the first four eigenvalues \( \lambda_{1}, \lambda_{2}, \lambda_{3} \), and \( \lambda_{4} \). \[ y^{\prime \prime}+\lambda y=0, \quad y(0)=0, \quad y(1)-\frac{1}{2} y^{\prime}(1)=0 \]


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Let us solve this under 3 cases possible Case 1: Let ?=0 Then the auxiliary equation is m2=0 And It's solution is m1=m2=0 The general solution will be
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