LabVIEW task. Design a VI that approximates the output of an ODE for

any given initial value, step size, and any given $x.$ Your GUI should have:

$y_0($initial value$),x($a value at which the target $y$ is to be computed$),h$

$($step size$),$ and the output value of the equation $($in the example, $x=3,$ so

the output is $y_3).$ The ODE to be solved is given as follows:

$\frac{dy}{dx}=3e^{-x}-0\mathrm{.}4y,$ with $y_0=5,$ step size $h=1\mathrm{.}5,$ and find $y_3$

where $y_0$ the value of $y$ when $x=0,$ and $y_3$ is the value of $y$ when $x=3$

$4^{th}$ order

Runge$-$Kutta

Approximation

$y_{i+1}=y_i+\frac{1}{6}h(k_1+2k_2+2k_3+k_4)$

$k_1=f(x_i,y_i)$

$k_2=f(x_i+0\mathrm{.}5h,y_i+0\mathrm{.}5k_{1}h)$

$k_3=f(x_i+0\mathrm{.}5h,y_i+0\mathrm{.}5k_{2}h)$

$k_4=f(x_i+h,y_i+k_{3}h)$