Wednesday, December 24, 2014

Advanced Math Solutions – Ordinary Differential Equations Calculator

Differential equations contain derivatives, solving the equation involves integration (to get rid of the derivatives). We will cover the most common methods to solve ODE’s: linear, separable and Bernoulli.
  • Linear first order equation is an ODE of the form y'(x)+p(x)y(x)=q(x)
  • Separable equation is an ODE of the form N(y)dy=M(x)dx
  • Bernoulli equation is an ODE of the form y'+p(x)y=q(x)y^n

You have first to identify the ODE type (can be tricky); then simply follow the steps as described below. 


Here’s an example of a separable equation (click here):


Simply solve by integrating both sides of the equation:



Here’s an example of a linear first order equation (click here):  


Steps to find the integration factor:



Here’s an example of a Bernoulli equation (click here):



In the next post we will take a closer look at each of the ODE types.

Cheers,

Michal

12 comments:

  1. Thanks my friend.This is a good post about differential equations and their solutions. But, it will be better if you write about homogeneous differential equations which is also important part of ODE. Homogeneous differential equations are in the form dy/dx=f(y/x).

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