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How many arbitrary constants will be there in the general solution of a second order differential equation?
- a)3
- b)4
- c)2
- d)1
Correct answer is option 'C'. Can you explain this answer?
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How many arbitrary constants will be there in the general solution of ...
The number of arbitrary constants in a general solution of a nth order differential equation is n.
Therefore, the number of arbitrary constants in the general solution of a second order D.E is 2.
Therefore, the number of arbitrary constants in the general solution of a second order D.E is 2.
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How many arbitrary constants will be there in the general solution of ...
Explanation:
To understand the number of arbitrary constants in the general solution of a second-order differential equation, let's first review the concept of a general solution.
General solution of a differential equation:
The general solution of a differential equation is a solution that contains all possible solutions of the equation. It typically contains arbitrary constants that can take any value, which allows for a wide range of solutions.
Second-order differential equation:
A second-order differential equation involves a second derivative (d²y/dx²) of a dependent variable y with respect to an independent variable x. It can be expressed in the form:
a(d²y/dx²) + b(dy/dx) + cy = f(x)
Order of a differential equation:
The order of a differential equation is the highest order of derivative present in the equation. For a second-order differential equation, the highest order of derivative is 2.
Number of arbitrary constants:
The number of arbitrary constants in the general solution of a second-order differential equation is equal to the order of the equation. In this case, since we have a second-order differential equation, the number of arbitrary constants in the general solution will be 2.
Therefore, the correct answer is option C - 2.
To understand the number of arbitrary constants in the general solution of a second-order differential equation, let's first review the concept of a general solution.
General solution of a differential equation:
The general solution of a differential equation is a solution that contains all possible solutions of the equation. It typically contains arbitrary constants that can take any value, which allows for a wide range of solutions.
Second-order differential equation:
A second-order differential equation involves a second derivative (d²y/dx²) of a dependent variable y with respect to an independent variable x. It can be expressed in the form:
a(d²y/dx²) + b(dy/dx) + cy = f(x)
Order of a differential equation:
The order of a differential equation is the highest order of derivative present in the equation. For a second-order differential equation, the highest order of derivative is 2.
Number of arbitrary constants:
The number of arbitrary constants in the general solution of a second-order differential equation is equal to the order of the equation. In this case, since we have a second-order differential equation, the number of arbitrary constants in the general solution will be 2.
Therefore, the correct answer is option C - 2.
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How many arbitrary constants will be there in the general solution of a second order differential equation?a)3b)4c)2d)1Correct answer is option 'C'. Can you explain this answer?
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How many arbitrary constants will be there in the general solution of a second order differential equation?a)3b)4c)2d)1Correct answer is option 'C'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about How many arbitrary constants will be there in the general solution of a second order differential equation?a)3b)4c)2d)1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many arbitrary constants will be there in the general solution of a second order differential equation?a)3b)4c)2d)1Correct answer is option 'C'. Can you explain this answer?.
How many arbitrary constants will be there in the general solution of a second order differential equation?a)3b)4c)2d)1Correct answer is option 'C'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about How many arbitrary constants will be there in the general solution of a second order differential equation?a)3b)4c)2d)1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many arbitrary constants will be there in the general solution of a second order differential equation?a)3b)4c)2d)1Correct answer is option 'C'. Can you explain this answer?.
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