Substituting the exponential trial solution into the homogeneous equation (Q1662): Difference between revisions
Jump to navigation
Jump to search
Add content item |
Add content item |
||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
| Property / LaTeX source | |||
| Property / LaTeX source: y=e^{rx},\\quad y'=r\\,e^{rx},\\quad y''=r^{2}\\,e^{rx};\\qquad y''+a\\,y'+b\\,y=\\bigl(r^{2}+a\\,r+b\\bigr)e^{rx}=0\\ \\Rightarrow\\ r^{2}+a\\,r+b=0,\\quad e^{rx}\\neq 0 / rank | |||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
Normal rank | |||
| Property / LaTeX source | |||
y=e^{rx},\\quad y'=r\\,e^{rx},\\quad y''=r^{2}\\,e^{rx};\\qquad y''+a\\,y'+b\\,y=\\bigl(r^{2}+a\\,r+b\\bigr)e^{rx}=0\\ \\Rightarrow\\ r^{2}+a\\,r+b=0,\\quad e^{rx}\\neq 0 | |||
| Property / LaTeX source: y=e^{rx},\\quad y'=r\\,e^{rx},\\quad y''=r^{2}\\,e^{rx};\\qquad y''+a\\,y'+b\\,y=\\bigl(r^{2}+a\\,r+b\\bigr)e^{rx}=0\\ \\Rightarrow\\ r^{2}+a\\,r+b=0,\\quad e^{rx}\\neq 0 / rank | |||
Normal rank | |||
Latest revision as of 07:28, 4 September 2026
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Substituting the exponential trial solution into the homogeneous equation |
No description defined |
Statements
y=e^{rx},\\quad y'=r\\,e^{rx},\\quad y''=r^{2}\\,e^{rx};\\qquad y''+a\\,y'+b\\,y=\\bigl(r^{2}+a\\,r+b\\bigr)e^{rx}=0\\ \\Rightarrow\\ r^{2}+a\\,r+b=0,\\quad e^{rx}\\neq 0
0 references