Find the length of the curve. y = 2 x 3 / 2 ,  from …

Find the length of the curve. y = 2 x 3 / 2 ,  from  x = 0  to  x = 5 4 {“version”:”1.1″,”math”:”y=2x^{3/2}, \text{ from } x=0 \text{ to } x=\frac{5}{4}”} Note:  L = ∫ a b ( 1 + ( f ′ ( x ) ) 2 ) d x {“version”:”1.1″,”math”:”L=\int_a^b\left(\sqrt{1+(f'(x))^2}\right)dx”}

Consider the initial value problem (IVP) with initial condi…

Consider the initial value problem (IVP) with initial conditions y(0) = y'(0) = 1 and y”(0) = y”'(0) = 0. (a) Write this as a system of four 1st order ordinary differential equations (ODEs). [9 points] (b) Change (any) one feature of the ODE to convert it into a nonlinear ODE. [2 points] (c) Change the initial conditions to (any) boundary conditions and convert the IVP to a boundary value problem (BVP). [4 points]

The slope fields f(t, y) for two IVPs y’ = f(t, y) are shown…

The slope fields f(t, y) for two IVPs y’ = f(t, y) are shown below.   (a) Trace (approximately) the solution on both figures if the initial condition is y(t = 0) = 0.1 (indicated by the star). If you are taking the quiz online, then write down the approximate values of y(t) at four different points in the domain 0 < t < 10 [9 points] (b) For which one of the two problems would a method like RK4 (classical explicit 4th order Runge-Kutta) be more appropriate? Why? [3 points] (c) What method would you recommend for the other problem? Why? [3 points]