13. Intro to Differential Equations

In Exercises 39–42, use Euler’s method with the specified step size to estimate the value of the solution at the given point x*. Find the value of the exact solution at x*.

y′ = √x/y, y > 0, y(0) = 1, dx = 0.1, x* = 1

In Exercises 39–42, use Euler’s method with the specified step size to estimate the value of the solution at the given point x*. Find the value of the exact solution at x*.

y' = 1 + y², y(0) = 0, dx = 0.1, x* = 1

25. First-order chemical reactions In some chemical reactions, the rate at which the amount of a substance changes with time is proportional to the amount present. For the change of δ-gluconolactone into gluconic acid, for example,

dy/dt = -0.6y

when t is measured in hours. If there are 100 grams of δ-gluconolactone present when t=0, how many grams will be left after the first hour?