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]