Differential Equations Test

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Differential Equations Test - 1

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Question 1
1 / -0

Differential equations are equations containing functions y = f(x), g(x) and

A
derivatives of y

B
maxima of y

C
minima of y

D
tangent of y at zero

Solution

Explanation:

Differential equations are equations containing functions y = f(x), g(x) and derivatives of y with respect to x.
Question 2
1 / -0

Order of a differential equation is defined as

A
the number of derivative terms

B
the number of constant terms

C
the order of the lowest order derivative ofthe dependent variable

D
the order of the highest order derivative of the dependent variable

Solution

Explanation:

Order of a differential equation is defined as the order of the highest order derivative of the dependent variable present in the differential equation.
Question 3
1 / -0

Degree of a differential equation, when the equation is polynomial equation in y′ is

A
Lowest power (positive integral index) of the highest order derivative in the given differential equation.

B
Highest (positive integral index) of the lowest order derivative in the given differential equation.

C
Lowest power (positive integral index) of the lowest order derivative in the given differential equation.

D
Highest power (positive integral index) of the highest order derivative in the given differential equation.

Solution

Explanation:

The power or index of the highest ordered derivative in the polynomial is the degree of the differential equation provided equation is in the standard form.
Question 4
1 / -0

Find the order and degree of y′′′+ y²+ e^y ′= 0 is

A
4, degree undefined

B
2, degree undefined

C
1, degree undefined

D
3, degree undefined

Solution

Explanation:

Order = 3 ,Since the highest order derivative is y′′′ but degree cannot be defined ,because the deriative term y’ is present in exponential form.
Question 5
1 / -0

Determine order and degree (if defined) of y’ + 5y = 0

A
1, 1

B
2, 1

C
1, 2

D
1,degree undefined

Solution

Explanation:

Order = 1 , degree = 1. Since the equation has the highest derivative as y' and its power is 1