Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:partial_differential_equations
|
| gptkbp:alsoKnownAs |
gptkb:Euler–Cauchy_equation
|
| gptkbp:application |
engineering
physics |
| gptkbp:category |
ordinary differential equation
|
| gptkbp:field |
gptkb:partial_differential_equations
gptkb:mathematics |
| gptkbp:form |
a x^2 y'' + b x y' + c y = 0
|
| gptkbp:generalSolution |
y(x) = x^r
|
| gptkbp:hasCharacteristicEquation |
ar(r-1) + br + c = 0
|
| gptkbp:hasVariableCoefficients |
true
|
| gptkbp:namedAfter |
gptkb:Augustin-Louis_Cauchy
gptkb:Leonhard_Euler |
| gptkbp:order |
second order
|
| gptkbp:solvedBy |
power function solutions
reduction to constant-coefficient equation |
| gptkbp:type |
linear differential equation
|
| gptkbp:bfsParent |
gptkb:Augustin-Louis_Cauchy
|
| gptkbp:bfsLayer |
5
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cauchy–Euler equation
|