Quick Review of Differential Equation
1st Order ODE
=>Linear and Separable
2nd Order Linear Homogeneous ODE with constant coefficient
─────(2)
where
Characteristic of Equation (2)
1st Order ODE
* Linear ODE
-> Integration Factor
* Separable ODE
-> separating the variable
* Homogeneous
-> make it to a separable ODE
* Other ODE
Approximation
-> Euler Method..
Example-> Integration Factor
* Separable ODE
-> separating the variable
* Homogeneous
-> make it to a separable ODE
* Other ODE
Approximation
-> Euler Method..
=>Linear and Separable
Sol. 1
Linear solution
Multiplying by Integrating factor..
where C is a arbitrary constant
Sol. 2
separable solution
integrate both side..
Linear solution
Multiplying by Integrating factor..
where C is a arbitrary constant
Sol. 2
separable solution
integrate both side..
2nd Order Linear Homogeneous ODE with constant coefficient
where
Characteristic of Equation (2)
*Case I
Distinct real root
General Solution of (2)
*Case II
Repeated real root
General solution of (2)
*Case III
Complex roots
General solution of (2)
Distinct real root
General Solution of (2)
*Case II
Repeated real root
General solution of (2)
*Case III
Complex roots
General solution of (2)
