Homogeneous function: Difference between revisions

Revision as of 00:57, 3 September 2022

Revision as of 13:56, 9 September 2022

Line 121:

The results from Euler's theorem by derivating the partial differential equation with respect to one variable.

In the case of a function of a single real variable (<math>n = 1</math>), the theorem implies that a continuously differentiable and poxitivelypositively homogeneous function of degree {{mvar|k}} has the form <math>f(x)=c_+ x^k</math> for <math>x>0</math> and <math>f(x)=c_- x^k</math> for <math>x<0.</math> The constants <math>c_+</math> and <math>c_+</math>are not necessarily the same, as it is the case for the [[absolute value]].

==Application to differential equations==