The numbers of arbitrary constants in the general solution of a differential equation of fourth order are:
The numbers of arbitrary constants in the general solution of a differential equation of fourth order are:
- 0
- 2
- 3
- 4
The Correct Option is D
Solution and Explanation
We know that the number of constants in the general solution of a differential equation of order n is equal to its order.
Therefore, the number of constants in the general equation of fourth order differential equation is four.
Hence, the correct answer is (D): 4
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Determine whether each of the following relations are reflexive, symmetric, and transitive.
- Relation R in the set A={1,2,3,...13,14} defined as R={(x,y): 3x-y=0}.
- Relation R in the set of N natural numbers defined as R={(x,y): y=x+5 and x<4}.
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- Relation R in the set of Z integers defined as R={(x,y): x-y is an integer}
- Relation R in the set of human beings in a town at a particular time given by
- R={(x,y): x and y work at same place}
- R={(x,y): x and y live in the same locality}
- R={(x,y): x is exactly 7 am taller that y}
- R={(x,y): x is wife of y}
- R={(x,y):x is father of y}
Show that the relation R in the set R of real numbers, defined as
R = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive.Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
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- Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y-cos y=x :(ysin y+cosy+x)y'=y
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- Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:\(y=\sqrt{a^2-x^2}\,\,\, x∈(-a,a) :x+y (\frac{dy}{dx}) =0(y≠0)\)
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Concepts Used:
General Solutions to Differential Equations
A relation between involved variables, which satisfy the given differential equation is called its solution. The solution which contains as many arbitrary constants as the order of the differential equation is called the general solution and the solution free from arbitrary constants is called particular solution.
For example,
Read More: Formation of a Differential Equation