Variation of parameters applied to y''-3y'+2y=e^x (Q1648): Difference between revisions
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| Property / instance of: mathematical expression / rank | |||
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| Property / LaTeX source: y_{1}=e^{x},\\quad y_{2}=e^{2x},\\quad W=y_{1}y_{2}'-y_{2}y_{1}'=e^{3x};\\qquad u_{1}'=-\\frac{y_{2}\\,g}{W}=-1,\\quad u_{2}'=\\frac{y_{1}\\,g}{W}=e^{-x} / rank | |||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
Normal rank | |||
| Property / LaTeX source | |||
y_{1}=e^{x},\\quad y_{2}=e^{2x},\\quad W=y_{1}y_{2}'-y_{2}y_{1}'=e^{3x};\\qquad u_{1}'=-\\frac{y_{2}\\,g}{W}=-1,\\quad u_{2}'=\\frac{y_{1}\\,g}{W}=e^{-x} | |||
| Property / LaTeX source: y_{1}=e^{x},\\quad y_{2}=e^{2x},\\quad W=y_{1}y_{2}'-y_{2}y_{1}'=e^{3x};\\qquad u_{1}'=-\\frac{y_{2}\\,g}{W}=-1,\\quad u_{2}'=\\frac{y_{1}\\,g}{W}=e^{-x} / rank | |||
Normal rank | |||
Latest revision as of 19:39, 3 September 2026
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Variation of parameters applied to y''-3y'+2y=e^x |
No description defined |
Statements
y_{1}=e^{x},\\quad y_{2}=e^{2x},\\quad W=y_{1}y_{2}'-y_{2}y_{1}'=e^{3x};\\qquad u_{1}'=-\\frac{y_{2}\\,g}{W}=-1,\\quad u_{2}'=\\frac{y_{1}\\,g}{W}=e^{-x}
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