[Steps Shown] Given that y_1(x)=e^2x cos x and y_2(x)=e^2x sin x are solutions to the homogeneous equation y''-4y'+5y=0 find the solutions to this equation
Question: Given that \({{y}_{1}}\left( x \right)={{e}^{2x}}\cos x\) and \({{y}_{2}}\left( x \right)={{e}^{2x}}\sin x\) are solutions to the homogeneous equation
\[y''-4y'+5y=0\]find the solutions to this equation that satisfy the following initial conditions:
- \(y\left( 0 \right)=2,\,\,y'\left( 0 \right)=1\)
- \(y\left( \pi \right)=4{{e}^{2\pi }},\,\,\,y'\left( \pi \right)=5{{e}^{2\pi }}\)
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Deliverable: Word Document 
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