1. Solve the ODE by using variation of parameters method, and y=e^x is one of the homogenous solutions. (20%) 2xy'' + (1 - 4x)y' + (2x - 1)y = e^x

2. \( \sigma_{ij} = \begin{bmatrix} \sigma_{xx} & \tau_{xy} & \tau_{xz} \\ \tau_{yx} & \sigma_{yy} & \tau_{yz} \\ \tau_{zx} & \tau_{zy} & \sigma_{zz} \end{bmatrix} = \begin{bmatrix} 3 & 0 & -2 \\ 0 & 2 & 0 \\ -2 & 0 & 0 \end{bmatrix} \) is a stress tensor, find the principal stresses and the unit vectors of principal directions by using eigenvalues and eigenvectors. (20%)

1. Solve the ODE by using variation of parameters method, and \( y=e^x \) is one of the homogenous solutions. (20%) \[ 2xy'' + (1 - 4x)y' + (2x - 1)y = e^x \]

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