Mathematics Exam > Mathematics Questions > If the general solutions of a differential eq...
Start Learning for Free
If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation is
- a)1, 2
- b)2, 1
- c)1, 3
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If the general solutions of a differential equation are (y + c)2 = cx,...
There will only one constant in the first-order differential equation. Differentiating the given equation.
Putting the value of c in Eq. (1) and simplifying we will get a first-order and second-degree equation. Hence, (A) is the correct answer.
Most Upvoted Answer
If the general solutions of a differential equation are (y + c)2 = cx,...
To determine the order and degree of a differential equation, we need to analyze the given general solution. Let's break down the given general solution step by step:
General solution: (y - c)^2 = cx
1. Expanding the equation:
y^2 - 2cy + c^2 = cx
2. Rearranging the terms:
y^2 - 2cy - cx + c^2 = 0
Now, let's analyze the equation to determine its order and degree.
Order of a Differential Equation:
The order of a differential equation is determined by the highest derivative present in the equation. In this case, we don't see any derivatives explicitly mentioned in the general solution. However, we can rewrite the equation in differential form:
dy/dx = (2cy - c^2 + cx)/x
Here, we have the first derivative dy/dx present. Hence, the order of the differential equation is 1.
Degree of a Differential Equation:
The degree of a differential equation is determined by the highest power of the highest derivative present in the equation. In this case, we can see that the highest power of the highest derivative (dy/dx) is 1. However, we also have the term y^2 present in the equation.
To handle this situation, we can express y^2 as (dy/dx)^2 and rewrite the equation as:
(dy/dx)^2 - 2cy - cx + c^2 = 0
Now, we can see that the highest power of the highest derivative is 2, which corresponds to the quadratic term (dy/dx)^2. Hence, the degree of the differential equation is 2.
Therefore, the order and degree of the given differential equation are 1 and 2, respectively. Hence, the correct answer is option A) 1, 2.
General solution: (y - c)^2 = cx
1. Expanding the equation:
y^2 - 2cy + c^2 = cx
2. Rearranging the terms:
y^2 - 2cy - cx + c^2 = 0
Now, let's analyze the equation to determine its order and degree.
Order of a Differential Equation:
The order of a differential equation is determined by the highest derivative present in the equation. In this case, we don't see any derivatives explicitly mentioned in the general solution. However, we can rewrite the equation in differential form:
dy/dx = (2cy - c^2 + cx)/x
Here, we have the first derivative dy/dx present. Hence, the order of the differential equation is 1.
Degree of a Differential Equation:
The degree of a differential equation is determined by the highest power of the highest derivative present in the equation. In this case, we can see that the highest power of the highest derivative (dy/dx) is 1. However, we also have the term y^2 present in the equation.
To handle this situation, we can express y^2 as (dy/dx)^2 and rewrite the equation as:
(dy/dx)^2 - 2cy - cx + c^2 = 0
Now, we can see that the highest power of the highest derivative is 2, which corresponds to the quadratic term (dy/dx)^2. Hence, the degree of the differential equation is 2.
Therefore, the order and degree of the given differential equation are 1 and 2, respectively. Hence, the correct answer is option A) 1, 2.
Free Test
FREE
| Start Free Test |
Community Answer
If the general solutions of a differential equation are (y + c)2 = cx,...
There will only one constant in the first-order differential equation. Differentiating the given equation.
Putting the value of c in Eq. (1) and simplifying we will get a first-order and second-degree equation. Hence, (A) is the correct answer.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer?
Question Description
If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the general solutions of a differential equation are (y + c)2 = cx, where c is an arbitrary constant, then the order and degree of differential equation isa)1, 2b)2, 1c)1, 3d)None of theseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup