Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
partial differential equations
|
| gptkbp:alsoKnownAs |
gptkb:Cauchy-Euler_equation
|
| gptkbp:application |
applied mathematics
engineering physics |
| gptkbp:characteristicEquation |
ar(r-1) + br + c = 0
|
| gptkbp:field |
gptkb:mathematics
partial differential equations |
| gptkbp:firstPublished |
18th century
|
| gptkbp:generalSolution |
y(x) = C1 x^{r1} + C2 x^{r2} (for distinct roots)
y(x) = x^r (C1 + C2 ln x) (for repeated roots) |
| gptkbp:hasEquation |
a x^2 y'' + b x y' + c y = 0
|
| https://www.w3.org/2000/01/rdf-schema#label |
Euler-Cauchy equation
|
| gptkbp:namedAfter |
gptkb:Augustin-Louis_Cauchy
gptkb:Leonhard_Euler |
| gptkbp:order |
second order
|
| gptkbp:solvedBy |
reduction to constant-coefficient equation
substitution y = x^r |
| gptkbp:type |
linear ordinary differential equation
|
| gptkbp:variableCoefficients |
yes
|
| gptkbp:bfsParent |
gptkb:Cauchy-Euler_equation
|
| gptkbp:bfsLayer |
7
|