(Solved): 3. Find the general solutions of the following differential equation \[ \begin{aligned} y^{\prime \ ...

3. Find the general solutions of the following differential equation \[ \begin{aligned} y^{\prime \prime}(x)-2 y^{\prime}(x)+y(x) & =\frac{e^{x}}{\sqrt{x}} \\ y^{\prime \prime}(x)+2 y^{\prime}(x)+y(x) & =\frac{\sqrt{x}}{e^{x}} \\ y^{\prime \prime}(x)-2 y^{\prime}(x)+y(x) & =\frac{x}{e^{x}} \end{aligned} \]