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प्रश्न
F(x, y) = `(x^2 + y^2)/(x - y)` is a homogeneous function of degree 1.
पर्याय
True
False
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उत्तर
This statement is True.
Explanation:
Because f(λx, λy) = λ1f(x, y).
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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). To solve a homogeneous differential equation of the type `dy/dx` = F(x, y) = `g(y/x)`, we make the substitution y = vx and then separate the variables. |
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