Write a general$-$purpose solver for systems of ODEs as a MATLAB function implementing both the $($i$)$ explicit Euler's method and $($ii$)$ implicit Euler's method. It is recommended that you follow the input$-$output convention of built$-$in MATLAB solvers, e$.$g$.,$ define your solver as

function $\backslash ([$t$,$ x$]=\backslash )$ solver $($func$,$ tspan, $\backslash ($ x $0,$ h $\backslash ))$

where func is the function of inputs $\backslash (($t$,$ x$)\backslash )$ defining the right$-$hand side of the ODE, and $\backslash ($ h $\backslash )$ is the time step.

When implementing the implicit Euler's method, you can make use of the built$-$in MATLAB solver fsolve for systems of nonlinear equations.

Describe your algorithm and demonstrate its performance on a simple test Initial Value Problem of your choice.