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Linear second order ordinary differential equation is non homogeneous if
- a)there is no constant in equation
- b)solution is zero
- c)solution has some value
- d)independent variable is present
Correct answer is option 'C'. Can you explain this answer?
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Linear second order ordinary differential equation is non homogeneous ...
Linear second order ordinary differential equation is non homogeneous if
Linear second order ordinary differential equation is of the form:
$$\frac{d^2y}{dx^2}+p(x)\frac{dy}{dx}+q(x)y=r(x)$$
where $p(x)$, $q(x)$ and $r(x)$ are functions of $x$.
Non-homogeneous equation means that there is a non-zero function on the right-hand side of the equation.
Solution is not zero
If the solution to the differential equation is zero, then we can say that the equation is homogeneous. This is because a homogeneous equation has a trivial solution of $y=0$. So, if the solution is not zero, then we can say that the equation is non-homogeneous.
Independent variable is present
The presence of the independent variable $x$ does not determine whether an equation is homogeneous or non-homogeneous. It is possible to have both homogeneous and non-homogeneous equations that contain the independent variable.
No constant in equation
The presence or absence of a constant in the equation does not determine whether it is homogeneous or non-homogeneous. This is because both homogeneous and non-homogeneous equations can contain constants.
Solution has some value
If the solution to the differential equation has some value, then we can say that the equation is non-homogeneous. This is because a homogeneous equation has a trivial solution of $y=0$, which means that the solution has no value other than zero.
Conclusion
Therefore, the correct option is C) solution has some value. If the solution to a linear second order ordinary differential equation has some value, then we can say that the equation is non-homogeneous.
Linear second order ordinary differential equation is of the form:
$$\frac{d^2y}{dx^2}+p(x)\frac{dy}{dx}+q(x)y=r(x)$$
where $p(x)$, $q(x)$ and $r(x)$ are functions of $x$.
Non-homogeneous equation means that there is a non-zero function on the right-hand side of the equation.
Solution is not zero
If the solution to the differential equation is zero, then we can say that the equation is homogeneous. This is because a homogeneous equation has a trivial solution of $y=0$. So, if the solution is not zero, then we can say that the equation is non-homogeneous.
Independent variable is present
The presence of the independent variable $x$ does not determine whether an equation is homogeneous or non-homogeneous. It is possible to have both homogeneous and non-homogeneous equations that contain the independent variable.
No constant in equation
The presence or absence of a constant in the equation does not determine whether it is homogeneous or non-homogeneous. This is because both homogeneous and non-homogeneous equations can contain constants.
Solution has some value
If the solution to the differential equation has some value, then we can say that the equation is non-homogeneous. This is because a homogeneous equation has a trivial solution of $y=0$, which means that the solution has no value other than zero.
Conclusion
Therefore, the correct option is C) solution has some value. If the solution to a linear second order ordinary differential equation has some value, then we can say that the equation is non-homogeneous.
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Linear second order ordinary differential equation is non homogeneous ifa)there is no constant in equationb)solution is zeroc)solution has some valued)independent variable is presentCorrect answer is option 'C'. Can you explain this answer? for Engineering Mathematics 2024 is part of Engineering Mathematics preparation. The Question and answers have been prepared according to the Engineering Mathematics exam syllabus. Information about Linear second order ordinary differential equation is non homogeneous ifa)there is no constant in equationb)solution is zeroc)solution has some valued)independent variable is presentCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Engineering Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Linear second order ordinary differential equation is non homogeneous ifa)there is no constant in equationb)solution is zeroc)solution has some valued)independent variable is presentCorrect answer is option 'C'. Can you explain this answer?.
Linear second order ordinary differential equation is non homogeneous ifa)there is no constant in equationb)solution is zeroc)solution has some valued)independent variable is presentCorrect answer is option 'C'. Can you explain this answer? for Engineering Mathematics 2024 is part of Engineering Mathematics preparation. The Question and answers have been prepared according to the Engineering Mathematics exam syllabus. Information about Linear second order ordinary differential equation is non homogeneous ifa)there is no constant in equationb)solution is zeroc)solution has some valued)independent variable is presentCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Engineering Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Linear second order ordinary differential equation is non homogeneous ifa)there is no constant in equationb)solution is zeroc)solution has some valued)independent variable is presentCorrect answer is option 'C'. Can you explain this answer?.
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