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

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