Topic: Differential Equations (Test 1)



Topic: Differential Equations
Q.1
Differential equations are equations containing functions y = f(x), g(x) and
A. minima of y
B. maxima of y
C. derivatives of y
D. tangent of y at zero
Answer : Option C
Explaination / Solution:

Differential equations are equations containing functions y = f(x), g(x) and derivatives of y with respect to x.

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Q.2
The degree of the equationis
A. 1
B. 2
C. 0
D. 3
Answer : Option B
Explaination / Solution:

the power of the highest order derivative i.e . is 2.hence the degree 2

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Q.3
Determine order and degree (if defined) ofcos() = 0
A. 0,degree undefined
B. 2,degree undefined
C. 3,1
D. 1,degree undefined
Answer : Option B
Explaination / Solution:

order = 2, degree not defined, because the function dy/dx present in angle of cosine function.

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Q.4
General solution of a given differential equation
A. contains exactly one arbitrary constant
B. contains exactly two arbitrary constants
C. contains arbitrary constants depending on the order of the differential equation
D. does not contain arbitrary constants
Answer : Option C
Explaination / Solution:

The general solution of differential equation contains arbitrary constants equal to the order of differential equaition.

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Q.5
General solution of  is
A. y = 1 + Ae3x
B. y = 1 + Aex
C. y = 1 + Ae-x
D. y = B + Aex
Answer : Option C
Explaination / Solution:


It is of the form of linear differential equation.hence the solution is y X  IF =

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Q.6
General solution of 
A. tanx2=C(1ex)
B. tany2=C(1ex)
C. tany3=C(1ex)
D. tany
=C(1ex)
Answer : Option D
Explaination / Solution:



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Q.7
Find the particular solution of the differential equation , given that y = 0 and x = 0.
A. 4e3x+3e4y+7=0
B. 4e3x3e4y7=0
C. 4e3x+3e4y7=1
D. 4e3x+3e4y7=0
Answer : Option D
Explaination / Solution:



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Q.8
To form a differential equation from a given function
A. Differentiate the function successively as many times as the number of arbitrary constants inthe given function and eliminate the arbitrary constants.
B. Differentiate the function once and eliminate the arbitrary constants
C. Differentiate the function once and add values to arbitrary constants
D. Differentiate the function twice and eliminate the arbitrary constants
Answer : Option A
Explaination / Solution:

We shall differentiate the function equal to the number of arbitrary constant so that we get equations equal to arbitrary constant and then eliminate them to form a differential equation

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Q.9
Forming a differential equation representing the given family of curves by eliminating arbitrary constants a and b from y =  (a cosx + b sinx) yields the differential equation
A. y″ + 2y′ - 2y = 0
B. y″ – 2y′ - 2y = 0
C. y″ +2y′ + 2y = 0
D. y″ – 2y′ + 2y = 0
Answer : Option D
Explaination / Solution:



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Q.10
Find the equation of a curve passing through the point (0, –2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.
A. y3 x2= 4
B. y2 x2= 4
C. y3 x3= 4
D. y2 x3= 4
Answer : Option B
Explaination / Solution:



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