Reduction of order for ordinary differential equations (Q1991): Difference between revisions
Jump to navigation
Jump to search
Add content item |
Updated the item for Reduction of order for ordinary differential equations from Special:Update |
||
| (4 intermediate revisions by the same user not shown) | |||
| label / en | label / en | ||
Reduction of | Reduction of order for ordinary differential equations | ||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
| Property / LaTeX source | |||
| Property / LaTeX source: y^{(n)}=f(x,y,y',\\ldots,y^{(n-1)})\\ \\Longrightarrow\\ y_1=y,\\; y_2=y',\\;\\ldots,\\;y_n=y^{(n-1)},\\qquad \\begin{cases} y_1'=y_2 \\\\ y_2'=y_3 \\\\ \\vdots \\\\ y_n'=f(x,y_1,y_2,\\ldots,y_n) \\end{cases} / rank | |||
| Property / describes | |||
| Property / describes: Ordinary differential equation / rank | |||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
Normal rank | |||
| Property / LaTeX source | |||
F\\bigl(x,y,y',y'',\\ldots,y^{(n)}\\bigr)=0 \\Longrightarrow \\begin{cases} y_2=y_1' \\\\ y_3=y_2' \\\\ \\vdots \\\\ y_n=y_{n-1}' \\\\ y_n'=f(x,y_1,y_2,\\ldots,y_n) \\end{cases} | |||
| Property / LaTeX source: F\\bigl(x,y,y',y'',\\ldots,y^{(n)}\\bigr)=0 \\Longrightarrow \\begin{cases} y_2=y_1' \\\\ y_3=y_2' \\\\ \\vdots \\\\ y_n=y_{n-1}' \\\\ y_n'=f(x,y_1,y_2,\\ldots,y_n) \\end{cases} / rank | |||
Normal rank | |||
| Property / describes | |||
| Property / describes: Ordinary differential equation / rank | |||
Normal rank | |||
Latest revision as of 18:36, 10 October 2026
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Reduction of order for ordinary differential equations |
No description defined |
Statements
F\\bigl(x,y,y',y'',\\ldots,y^{(n)}\\bigr)=0 \\Longrightarrow \\begin{cases} y_2=y_1' \\\\ y_3=y_2' \\\\ \\vdots \\\\ y_n=y_{n-1}' \\\\ y_n'=f(x,y_1,y_2,\\ldots,y_n) \\end{cases}
0 references