State whether the following statement is True or False: A homogeneous differential equation is solved by substituting y = vx and integrating it - Mathematics and Statistics

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MCQ
True or False

State whether the following statement is True or False:   

A homogeneous differential equation is solved by substituting y = vx and integrating it

Options

  • True

  • False

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Solution

True

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Chapter 1.8: Differential Equation and Applications - Q.3

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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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