Usage 1: Differential Equations Ex 3 Separable Equations

Say this prayer: it helps!

St. Michael the Archangel defend us in battle. Be our protection against the wickedness and snares of the Devil. May God rebuke him, we humbly pray, and do thou most Heavenly host, by the power of God cast into hell Satan and all the evil spirits who roam around the world seeking the ruin of souls. Amen.

Separable Equations .... (by Separation of Variables)

Properties:

* .... know what they are right off hand.

* .... have method that we know to solve these equations directly.

We say that "an ordinary differential equation is separable if it is possible, by elementary algebraic manipulation, to arrange the equation so that all the dependent variables (usually the y variable) are on one side and all the independent variables (usually the x variable) are on the other side. The corresponding solution technique is called separation of variables."(S.G. Krantz, 2005)

Notice that integration is being done on each side of the equation.

Notice, also, that since our equation was of the first order that we have one constant.

You can go to DE Ex2 here...D.E. Ex2.

You can go to DE Ex1 here ...D.E. Ex1.