Differential Equations Test

Result

Differential Equations Test - 4

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Question 1
1 / -0

Function y = f(x) is said to satisfy a differential equation g(y, y’, y’’...) = h(x), if

A
y and its derivatives substituted in equation g (y, y’, y’’...) = h(x) yield L.H.S. = 0

B
y and its derivatives substituted in equation g (y, y’, y’’...) = h(x) yield L.H.S. ≠ R.H.S.

C
y and its derivatives substituted in equation g(y, y’, y’’...) =h(x) yield L.H.S. = R.H.S.

D
If h(x) = 0

Solution

Function y = f(x) is said to satisfy a differential equation g (y, y’, y’’...) =h(x) if y and its derivatives substituted in equation g(y, y’, y’’...) = h(x) yield L.H.S. = R.H.S.
Question 2
1 / -0

General solution of a given differential equation

A
contains exactly one arbitrary constant

B
contains arbitrary constants depending on the order of the differential equation

C
contains exactly two arbitrary constants

D
does not contain arbitrary constants

Solution

The general solution of differential equation contains arbitrary constants equal to the order of differential equation
Question 3
1 / -0

Particular solution of a given differential equation

A
can contain arbitrary constants

B
does not contain arbitrary constants

C
can contain exactly two arbitrary constants

D
can contain exactly one arbitrary constant

Solution

Particular solution of a given differential equation does not contain arbitrary constants i.e. a,b ,c etc since the value of those arbitrary can be found out by substituting the given values.
Question 4
1 / -0

The number of arbitrary constants in the general solution of a differential equation of fourth order are:

A
2

B
3

C
1

D
4

Solution

4, because the no. of arbitrary constants is equal to order of the differential equation.
Question 5
1 / -0

The number of arbitrary constants in the particular solution of a differential equation of third order are:

A
1

B
3

C
2

D
0

Solution

0, because the particular solution is free from arbitrary constants.