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The results from Euler's theorem by differentiating 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 positively 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_
==Application to differential equations==
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