Reduction of an nth-order equation to a first-order system (Q1991): Difference between revisions
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| 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 | |||
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} | |||
| 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 | |||
Normal rank | |||
| Property / describes | |||
| Property / describes: Ordinary differential equation / rank | |||
Normal rank | |||
Revision as of 14:09, 4 October 2026
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Reduction of an nth-order equation to a first-order system |
No description defined |
Statements
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}
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