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The differential equation d^2y/dx^2 +x^2 dy/dx +x^3 y=e^x
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?
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?
Most Upvoted Answer
The differential equation d^2y/dx^2 +x^2 dy/dx +x^3 y=e^xThe different...
Linearity of Differential Equations
Linear differential equations are equations in which the dependent variable and its derivatives appear in a linear manner. Non-linear differential equations involve products or powers of the dependent variable and its derivatives.
Degree of Differential Equations
The degree of a differential equation is the highest power of the highest-order derivative present in the equation. For example, a first-degree differential equation has the highest derivative raised to the power of 1.
Analysis of the Given Equation
The given differential equation is:
d^2y/dx^2 +x^2 dy/dx +x^3 y=e^x
1. The highest derivative present is the second derivative, making it a second-degree differential equation.
2. The terms involving y and its derivatives are linear (1st degree) since they do not involve products or powers of y or its derivatives.
3. The presence of x^2 dy/dx and x^3 y terms does not affect the linearity of the equation since they are multiplied by y or its derivative.
Conclusion
The given differential equation is a linear differential equation of second degree. It is not non-linear as it does not involve products or powers of y or its derivatives. The linearity and degree of the equation are crucial in determining the methods and techniques used to solve it.
Linear differential equations are equations in which the dependent variable and its derivatives appear in a linear manner. Non-linear differential equations involve products or powers of the dependent variable and its derivatives.
Degree of Differential Equations
The degree of a differential equation is the highest power of the highest-order derivative present in the equation. For example, a first-degree differential equation has the highest derivative raised to the power of 1.
Analysis of the Given Equation
The given differential equation is:
d^2y/dx^2 +x^2 dy/dx +x^3 y=e^x
1. The highest derivative present is the second derivative, making it a second-degree differential equation.
2. The terms involving y and its derivatives are linear (1st degree) since they do not involve products or powers of y or its derivatives.
3. The presence of x^2 dy/dx and x^3 y terms does not affect the linearity of the equation since they are multiplied by y or its derivative.
Conclusion
The given differential equation is a linear differential equation of second degree. It is not non-linear as it does not involve products or powers of y or its derivatives. The linearity and degree of the equation are crucial in determining the methods and techniques used to solve it.
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The differential equation d^2y/dx^2 +x^2 dy/dx +x^3 y=e^xThe 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?
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The differential equation d^2y/dx^2 +x^2 dy/dx +x^3 y=e^xThe 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? 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 d^2y/dx^2 +x^2 dy/dx +x^3 y=e^xThe 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? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The differential equation d^2y/dx^2 +x^2 dy/dx +x^3 y=e^xThe 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?.
The differential equation d^2y/dx^2 +x^2 dy/dx +x^3 y=e^xThe 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? 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 d^2y/dx^2 +x^2 dy/dx +x^3 y=e^xThe 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? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The differential equation d^2y/dx^2 +x^2 dy/dx +x^3 y=e^xThe 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?.
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