Share
Explore BrainMass

Introduction to Ordinary Differential Equations

(e^y + 1)^2 * e^-y dx + (e^x + 1) * e^-x dy = 0

An ordinary differential equation (ODE) is an equation that involves derivatives, but no partial derivatives. The "dx" and "dy" found in the equation denote the derivatives involved. We read these notations as "with respect to x" (dx) and "with respect to y" (dy). Their inclusion in the equation makes it possible for us to solve using integration.

When solving an ODE, the simplest approach is to group together the x terms and the y terms so that we might integrate "with respect to x" and "with respect to y."

Solution Preview

(e^y + 1)^2 * e^-y dx + (e^x + 1) * e^-x dy = 0

An ordinary differential equation (ODE) is an equation that involves derivatives, but no partial derivatives. The "dx" and "dy" found in the equation denote the derivatives involved. We read these notations as "with respect to x" (dx) and "with respect to y" (dy). Their inclusion in the equation makes it possible for us to solve using integration.

When solving an ODE, the simplest approach is to group together the x terms and the y terms so that we might integrate "with respect to x" and "with ...

Solution Summary

In this example you will find a simple ordinary differential equation solved step-by-step with full work shown.

$2.19