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प्रश्न
Which of the following is not a homogeneous function of x and y.
पर्याय
x2 + 2xy
2x – y
`cos^2 (y/x) + y/x`
sinx – cosy
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उत्तर
sinx – cosy
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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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