Solve {l}{(D-3)^{2}y=2e^{4x}quad[text{Guwaha}}{d^{2}y/dx^{2}-3(dy/dx)+2y=e^{5x}}{(D^2+D+1)y=e^-x}{(D^2+5D+6)y=e^2x}

$$\left. \begin{array} { l } { ( D - 3 ) ^ { 2 } y = 2 e ^ { 4 x } \quad [ \text { Guwaha } } \\ { d ^ { 2 } y / d x ^ { 2 } - 3 ( d y / d x ) + 2 y = e ^ { 5 x } } \\ { ( D ^ { 2 } + D + 1 ) y = e ^ { - x } } \\ { ( D ^ { 2 } + 5 D + 6 ) y = e ^ { 2 x } } \end{array} \right.$$

Solve for x (complex solution)

$$x=\frac{\ln(y\left(D-3\right)^{2})-\ln(2)}{4}+\frac{\pi n_{1}i}{2}$$

$$n_{1}\in \mathrm{Z}$$

$$y\neq 0\text{ and }D\neq 3$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2\ln(\sqrt{y}\left(3-D\right))-\ln(2)}{4}\text{, }&y\geq 0\text{ and }D<3\\x=\frac{2\ln(\sqrt{y}\left(D-3\right))-\ln(2)}{4}\text{, }&y\geq 0\text{ and }D>3\end{matrix}\right.$$