Differential Equations Test

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Differential Equations Test - 7

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Question 1
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Determine order and degree (if defined) of

A
2, degree undefined

B
3, degree undefined

C
4, degree undefined

D
1, degree undefined

Solution

Order = 4 , degree not defined , because the function y ’’’present in the angle of sine function.
Question 2
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General solution of sec² x tany dx + sec² y tan x dy = 0 is

A
tan x tan y = C

B
y = tan 2x tan y + C

C
y = tan x tan 2y + C

D
y = tanx² tan y + C

Solution
Question 3
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Find the particular solution for (x + y) dy + (x –y) dx = 0; y = 1 when x = 1

A

B

C

D

Solution
Question 4
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Variable separation method can be used to solve First Order, First Degree Differential Equations in which y ’is of the form.

A
y ’= h(x)g(y)

B
y² = sin (h(x))

C
y² = cos (g(y))

D
y³ = g(y)

Solution

Variable separation method can be used to solveFirst Order, First Degree Differential Equations in which y ’is of the form. y ’= h(x)g(y) i.e
Question 5
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A

B

C

D

Solution
Question 6
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Determine order and degree (if defined) of y ’+ 5y = 0

A
1,degree undefined

B
1, 1

C
1, 2

D
2, 1

Solution

Order = 1 , degree = 1.
Question 7
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General Solution of (e^x + e^-x ) dy - (e ^x - e^-x ) dx = 0

A
y = log(e^2x + e^−x ) + C

B
y = log(e^x + e^−x ) + C

C
y = (e^x + e^−x ) + C

D
y = log(e^−2x + e^−x ) + C

Solution
Question 8
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General solution of x

A

B

C

D

Solution
Question 9
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solution of {x cos (y/x) + ysin(y/x)} ydx = {ysin(y/x) - x cos (y/x)} xdy is

A

B

C

D

Solution
Question 10
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A
y = e^−2x +Ce^−3x

B
y = e^−2x −Ce^−5x

C
y = e^−3x −Ce^−3x

D
y = e^−2x −Ce^−3x

Solution
Question 11
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Determine order and degree (if defined) of

A
1,degree undefined

B
1, 2

C
2, 1

D
2, 2

Solution

Order = 2 , degree = 1.
Question 12
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General solution of y log y dx –x dy = 0

A
y = e^−cx

B
y = e^cx + e^−cx

C
y = e^cx

D
y² = e^cx

Solution
Question 13
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To form a differential equation from a given function

A
Differentiate thefunction successively as many times as the number of arbitrary constants inthe given function and eliminate the arbitrary constants.

B
Differentiate thefunction twice and eliminate the arbitrary constants

C
Differentiate thefunction once and eliminate the arbitrary constants

D
Differentiate thefunction once and add values to arbitrary constants

Solution

To form a differential equation from a given functionDifferentiate thefunction successively as many times as the number of arbitrary constants inthe given function and eliminate the arbitrary constants.i.e. the differential equation should be free from arbitrary constants.
Question 14
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A differential equation of the form y '= F(x,y) is homogeneous if

A
F(x,y) is a homogeneous function of degree one

B
F(x,y) is a homogeneous function of degree three

C
F(x,y) is a homogeneous function of degree two

D
F(x,y) is a homogeneous function of degree zero

Solution

A differential equation of the form y '= F(x,y) is homogeneous if F(x,y) is a homogeneous function of degree zero.
Question 15
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General solution of(1+x² ) dy+2xy dx = cot x dx(x ≠0) is

A

B

C

D

Solution