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The differential equation is a
(a) non-linear differential equation of first degree
(b) linear differential equation of first degree
(c) linear differential equation of second degree
(d) non-linear differential equation of second degree
2
2 3
2
+ +=
d y dy x
x xye?
(a) non-linear differential equation of first degree
(b) linear differential equation of first degree
(c) linear differential equation of second degree
(d) non-linear differential equation of second degree
2
2 3
2
+ +=
d y dy x
x xye?
Most Upvoted Answer
The differential equation is a (a) non-linear differential equation of...
Differential Equation Type:
Linear differential equation of second degree
Explanation:
- The given differential equation is in the form of \(x^2 \frac{dy}{dx} + x^3y = 2x\).
- It is a linear differential equation because it is linear in terms of the dependent variable \(y\) and its derivatives.
- It is of second degree because the highest power of the highest order derivative in the equation is 2.
- The equation can be rewritten in standard form as \(\frac{dy}{dx} + \frac{x}{y} = \frac{2}{x}\).
- The equation is linear because it is of the form \( \frac{dy}{dx} + P(x)y = Q(x) \), where \(P(x) = \frac{x}{y}\) and \(Q(x) = \frac{2}{x}\), both of which are functions of \(x\) only.
- The linearity of the equation allows for the use of standard methods of solution such as the method of integrating factors or separation of variables.
Linear differential equation of second degree
Explanation:
- The given differential equation is in the form of \(x^2 \frac{dy}{dx} + x^3y = 2x\).
- It is a linear differential equation because it is linear in terms of the dependent variable \(y\) and its derivatives.
- It is of second degree because the highest power of the highest order derivative in the equation is 2.
- The equation can be rewritten in standard form as \(\frac{dy}{dx} + \frac{x}{y} = \frac{2}{x}\).
- The equation is linear because it is of the form \( \frac{dy}{dx} + P(x)y = Q(x) \), where \(P(x) = \frac{x}{y}\) and \(Q(x) = \frac{2}{x}\), both of which are functions of \(x\) only.
- The linearity of the equation allows for the use of standard methods of solution such as the method of integrating factors or separation of variables.
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The differential equation is a (a) non-linear differential equation of first degree (b) linear differential equation of first degree (c) linear differential equation of second degree (d) non-linear differential equation of second degree 2 2 3 2 + += d y dy x x xye?
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The differential equation is a (a) non-linear differential equation of first degree (b) linear differential equation of first degree (c) linear differential equation of second degree (d) non-linear differential equation of second degree 2 2 3 2 + += d y dy x x xye? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The differential equation is a (a) non-linear differential equation of first degree (b) linear differential equation of first degree (c) linear differential equation of second degree (d) non-linear differential equation of second degree 2 2 3 2 + += d y dy x x xye? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The differential equation is a (a) non-linear differential equation of first degree (b) linear differential equation of first degree (c) linear differential equation of second degree (d) non-linear differential equation of second degree 2 2 3 2 + += d y dy x x xye?.
The differential equation is a (a) non-linear differential equation of first degree (b) linear differential equation of first degree (c) linear differential equation of second degree (d) non-linear differential equation of second degree 2 2 3 2 + += d y dy x x xye? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The differential equation is a (a) non-linear differential equation of first degree (b) linear differential equation of first degree (c) linear differential equation of second degree (d) non-linear differential equation of second degree 2 2 3 2 + += d y dy x x xye? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The differential equation is a (a) non-linear differential equation of first degree (b) linear differential equation of first degree (c) linear differential equation of second degree (d) non-linear differential equation of second degree 2 2 3 2 + += d y dy x x xye?.
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