Differential Equations Test

Result

Differential Equations Test - 3

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Question 1
1 / -0

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

Solution

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 order of the lowest order derivative of the dependent variable

B
the number of derivative terms

C
the order of the highest order derivative of the dependent variable

D
the number of constant terms

Solution

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

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

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

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

Solution

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
2, degree undefined

B
3, degree undefined

C
4, degree undefined

D
1, degree undefined

Solution

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

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

A
2, 1

B
1, 2

C
1, 1

D
1,degree undefined

Solution

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