Solve {l}{text{C.}y=(C_{1}+C_{2}t)e^-t}{text{7.}y^(4)-2y^primeprimeprime+5y^primeprime=0(quad)<0:p>langle0:prangle}

$$\left. \begin{array} { l } { \text { C. } y = ( C _ { 1 } + C _ { 2 } t ) e ^ { - t } } \\ { \text { 7. } y ^ { ( 4 ) } - 2 y ^ { \prime \prime \prime } + 5 y ^ { \prime \prime } = 0 ( \quad ) < 0 : p > \langle 0 : p \rangle } \end{array} \right.$$

Solve for y, C_1, C_2, t (complex solution)

$$y=\frac{C_{2}t+C_{1}}{e^{t}}$$

$$t\in \mathrm{C}$$

$$C_{1}\in \mathrm{C}$$

$$C_{2}\in \mathrm{C}$$

Solve for y, C_1, C_2, t

$$y=\frac{C_{2}t+C_{1}}{e^{t}}$$

$$t\in \mathrm{R}$$

$$C_{1}\in \mathrm{R}$$

$$C_{2}\in \mathrm{R}$$