Statements (20)
Predicate | Object |
---|---|
gptkbp:instanceOf |
partial differential equations
|
gptkbp:alsoKnownAs |
gptkb:Euler–Cauchy_equation
|
gptkbp:application |
engineering
physics |
gptkbp:category |
ordinary differential equation
|
gptkbp:field |
gptkb:mathematics
partial differential equations |
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
|
https://www.w3.org/2000/01/rdf-schema#label |
Cauchy–Euler equation
|
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
|