मराठी

F(x, y) = x2+y2x-y is a homogeneous function of degree 1. - Mathematics

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प्रश्न

F(x, y) = `(x^2 + y^2)/(x - y)` is a homogeneous function of degree 1.

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

This statement is True.

Explanation:

Because f(λx, λy) = λ1f(x, y).

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पाठ 9: Differential Equations - Solved Examples [पृष्ठ १९१]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12
पाठ 9 Differential Equations
Solved Examples | Q 23. (v) | पृष्ठ १९१

संबंधित प्रश्‍न

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An equation involving derivatives of the dependent variable with respect to the independent variables is called a differential equation. A differential equation of the form `dy/dx` = F(x, y) is said to be homogeneous if F(x, y) is a homogeneous function of degree zero, whereas a function F(x, y) is a homogeneous function of degree n if F(λx, λy) = λn F(x, y).

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  1. Show that (x2 – y2) dx + 2xy dy = 0 is a differential equation of the type `dy/dx = g(y/x)`. (2)
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