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=== <small> 8.0 Abstract <small> === | === <small> 8.0 Abstract <small> === | ||
| − | <font size="3px"> Slightly we are moving to our last tutorial for the introduction of ordinary differential equations. This tutorial will give three particular methods to solve ODEs in the second order, which was also mentioned in 5.0. </font> | + | <font size="3px"> Slightly we are moving to our last tutorial for the introduction of ordinary differential equations. This tutorial will give three particular methods to solve ODEs in the second order, which was also mentioned in 5.0. Theories are boring, we will be processing with sample questions. </font> |
'''<font size="4px"> 8.1 Reduction of Order Method </font>''' | '''<font size="4px"> 8.1 Reduction of Order Method </font>''' | ||
| − | <font size="3px"> | + | <font size="3px"> This method is often used to find a second solution of an ODE, provided that one solution is given. |
| + | |||
| + | '''Example:''' Consier the ODE <math>t^2 (lnt+1) \frac{d^2y}{dt^2} + t(2lnt+1) \frac{dy}{dt} -y=0</math>, one of the solutions is <math>y=\frac{1}{t}</math>. Find a second solution. | ||
Revision as of 17:20, 22 November 2017
Advanced Methods to Solve 2nd-Order ODEs
8.0 Abstract
Slightly we are moving to our last tutorial for the introduction of ordinary differential equations. This tutorial will give three particular methods to solve ODEs in the second order, which was also mentioned in 5.0. Theories are boring, we will be processing with sample questions.
8.1 Reduction of Order Method
This method is often used to find a second solution of an ODE, provided that one solution is given.
Example: Consier the ODE $ t^2 (lnt+1) \frac{d^2y}{dt^2} + t(2lnt+1) \frac{dy}{dt} -y=0 $, one of the solutions is $ y=\frac{1}{t} $. Find a second solution.
8.2 Cauchy-Euler Equation
8.3 Varation of Constant
8.4 Exercises
8.5 References
Institute of Natural and Mathematical Science, Massey University. (2017). 160.204 Differential Equations I: Course materials. Auckland, New Zealand.
Robinson, J. C. (2003). An introduction to ordinary differential equations. New York, NY., USA: Cambridge University Press.
