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A differential equation of first degree
- a)Is always linear
- b)Is of first order
- c)May or may not be linear
- d)Is never of first order but is linear always
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A differential equation of first degreea)Is always linearb)Is of first...
(i)(a) is not correct because a differential equation of first degree may not be linear. For example, the differential equation.
is of first degree but non-linear,
(ii) (b) is not correct because a differential equation of first, degree is not necessarily of first order. The differential equation (i) is of first, degree but of second order.
(iii) (d) is not correct because a differential equation of first degree may be of first order and may not be linear.
is of first degree but non-linear,
(ii) (b) is not correct because a differential equation of first, degree is not necessarily of first order. The differential equation (i) is of first, degree but of second order.
(iii) (d) is not correct because a differential equation of first degree may be of first order and may not be linear.
Most Upvoted Answer
A differential equation of first degreea)Is always linearb)Is of first...
(i)(a) is not correct because a differential equation of first degree may not be linear. For example, the differential equation.
is of first degree but non-linear,
(ii) (b) is not correct because a differential equation of first, degree is not necessarily of first order. The differential equation (i) is of first, degree but of second order.
(iii) (d) is not correct because a differential equation of first degree may be of first order and may not be linear.
is of first degree but non-linear,
(ii) (b) is not correct because a differential equation of first, degree is not necessarily of first order. The differential equation (i) is of first, degree but of second order.
(iii) (d) is not correct because a differential equation of first degree may be of first order and may not be linear.
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Community Answer
A differential equation of first degreea)Is always linearb)Is of first...
A differential equation of first degree can be either linear or nonlinear, depending on the nature of the equation. However, it is always of first order.
Explanation:
First Degree Differential Equation:
A differential equation of first degree is an equation that involves derivatives of a function up to the first order. It can be represented as:
dy/dx = f(x, y)
where y is the dependent variable, x is the independent variable, dy/dx represents the derivative of y with respect to x, and f(x, y) is a given function.
Linear Differential Equation:
A linear differential equation is an equation in which the dependent variable y and its derivatives appear in a linear form. It can be represented as:
a(x)dy/dx + b(x)y = g(x)
where a(x), b(x), and g(x) are given functions of x. The highest power of y and its derivatives in the equation is 1. This means that the equation is linear with respect to y and its derivatives.
Nonlinear Differential Equation:
A nonlinear differential equation is an equation in which the dependent variable y and its derivatives appear in a nonlinear form. This means that the equation may contain terms with powers of y and its derivatives other than 1. For example:
(dy/dx)^2 + y = x
In this equation, the term (dy/dx)^2 is nonlinear with respect to y and its derivative.
Conclusion:
From the above explanation, it is clear that a differential equation of first degree can be either linear or nonlinear. Therefore, option C (may or may not be linear) is the correct answer. However, it is always of first order, which means that the highest power of y and its derivatives in the equation is 1.
Explanation:
First Degree Differential Equation:
A differential equation of first degree is an equation that involves derivatives of a function up to the first order. It can be represented as:
dy/dx = f(x, y)
where y is the dependent variable, x is the independent variable, dy/dx represents the derivative of y with respect to x, and f(x, y) is a given function.
Linear Differential Equation:
A linear differential equation is an equation in which the dependent variable y and its derivatives appear in a linear form. It can be represented as:
a(x)dy/dx + b(x)y = g(x)
where a(x), b(x), and g(x) are given functions of x. The highest power of y and its derivatives in the equation is 1. This means that the equation is linear with respect to y and its derivatives.
Nonlinear Differential Equation:
A nonlinear differential equation is an equation in which the dependent variable y and its derivatives appear in a nonlinear form. This means that the equation may contain terms with powers of y and its derivatives other than 1. For example:
(dy/dx)^2 + y = x
In this equation, the term (dy/dx)^2 is nonlinear with respect to y and its derivative.
Conclusion:
From the above explanation, it is clear that a differential equation of first degree can be either linear or nonlinear. Therefore, option C (may or may not be linear) is the correct answer. However, it is always of first order, which means that the highest power of y and its derivatives in the equation is 1.
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A differential equation of first degreea)Is always linearb)Is of first orderc)May or may not be lineard)Is never of first order but is linear alwaysCorrect answer is option 'C'. Can you explain this answer?
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