Question

I’m trying to input a second order differential equation to solve into matlab over x = 0 to x =1. I can’t figure out how. Here’s the equation:

y” = 1 + 0.1 \sqrt{1+(y’)^2}

with initial conditions at zero.

Answer 1

Normally you solve higher-order equations by converting to a system of first order equations. Here, you would define:

y' = v
v' = 1 + 0.1 \sqrt{1 + v^2}

Define a function computing the right-hand side, and use ode45.

Note that this equation is solvable without much trouble in closed form, too, so should be a good test for how to do it.