Given differential equation:$\backslash [-2$y$\text{'}\text{'}+5$y$\text{'}+3$y $=\backslash$exp$(-0\mathrm{.}2$x$)\backslash ]$for $\backslash ($ x $\backslash )$ ranging from $0$ to $10.$Boundary conditions:$-\backslash ($ y$\text{'}(0)=1\backslash )$ is a Neumann boundary condition.$-\backslash ($ y$\text{'}(10)=-$y$(10)\backslash )$ is a mixed boundary condition.Solve this problem using the Neumann method and then solve it using the Dirichlet method for comparison. Check how the solution changes with different step sizes $\backslash ($ h $=1\backslash )$ or $\backslash ($ h $=0\mathrm{.}1\backslash ).$ Solve the problem manually without using code $($e$.$g$.,$ using the TDMA matrix method$).$