(Solved): 9. A solution basis for the equation \[ y^{\prime \prime}+4 y^{\prime}=0 \] is: (a) \( \left\{y_{1} ...

9. A solution basis for the equation \[ y^{\prime \prime}+4 y^{\prime}=0 \] is: (a) \( \left\{y_{1}=1, y_{2}=e^{4 x}\right\} \) (b) \( \left\{y_{1}=0, y_{2}=e^{4 r}\right\} \) (c) \( \left\{y_{1}=x, y_{2}=e^{-4 x}\right\} \) (d) \( \left\{y_{1}=1, y_{2}=e^{-4 x}\right\} \) (e) None of the above. 10. A solution basis for the equation \[ y^{\prime \prime}+4 y=0 \] is: (a) \( \left\{y_{1}=e^{2} x, y_{2}=e^{-2 r}\right\} \) (b) \( \left\{y_{1}=0, y_{2}=e^{4 x}\right\} \) (c) \( \left\{y_{1}=\cos 2 x, y_{2}=\sin 2 x\right\} \) (d) \( \left\{y_{1}=\cos 4 x, y_{2}=\sin 4 x\right\} \) (e) None of the above. 11. Which of the following equations does not have \( y=e^{2 x} \) as a solution? (a) \( y^{\prime \prime}-5 y^{\prime}+6 y=0 \) (b) \( y^{\prime \prime}+2 y^{\prime}-8 y=0 \) (c) \( y^{\prime \prime}-3 y^{\prime}-10 y=0 \) (d) \( y^{\prime \prime}-2 y^{\prime}=0 \) (e) All of the above. 12. A fundamental set of solutions of \( y^{\prime \prime}-4 y^{\prime}+13 y=0 \) is: (a) \( \left\{e^{2 x} \cos 3 x, e^{2 x} \sin 3 x\right\} \) (b) \( \left\{e^{3 x} \cos 2 x, e^{3 x} \sin 2 x\right\} \) (c) \( \left\{e^{-2 x} \cos 3 x, e^{-2 x} \sin 3 x\right\} \) (d) \( \left\{e^{-3 x} \cos 2 x, e^{-3 x} \sin 2 x\right\} \) (e) None of the above.