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Solution for Differential Equation Worksheet

Solution for Differential Equation Worksheet
  • Page 1
 1.  
An equation that involves one or more derivatives of an unknown function is called a _______
a.
Linear equation
b.
Trignometric equation
c.
Differential equation
d.
Exponential equation
e.
Quadratic equation


Solution:

A differential equation is an equation that involves one or more derivatives of an unknown function.


Correct answer : (3)
 2.  
The highest exponent of the highest order derivative in a differential equation is the ______ of the differential equation.
a.
Degree
b.
Order
c.
Exponent
d.
Both A and B
e.
Both B and C


Solution:

The degree of the differential equation is the highest exponent of the highest order derivative in a differential equation


Correct answer : (1)
 3.  
The highest order derivative of the unknown function occuring in the differential equation is the ________ of the differential equation
a.
Power
b.
Order
c.
Degree
d.
Particular solution
e.
General solution


Solution:

The highest order derivative of the unknown function occuring in the differential equation is the order of the differential equation.


Correct answer : (2)
 4.  
What is the degree of the differential equation (d2ydx2)2 + x = y?
a.
2
b.
1
c.
4
d.
3


Solution:

(d2ydx2)2 + x = y
[Write the Differential equation.]

The highest exponent of the highest order derivative in the differential equation is the degree of the differential equation.

So, the degree of the differential equation is 2
[The highest order derivative is d2ydx2 whose exponent is 2.]


Correct answer : (1)
 5.  
Any function that satisfies a differential equation is known as the ________ of that differential equation.
a.
Degree
b.
Order
c.
General solution
d.
Particular solution
e.
Linear solution


Solution:

Any function that satisfies a differential equation is known as the particular solution of that differential equation


Correct answer : (4)
 6.  
What is the order of the differential equation d3ydt3 + tdydt+t2y = t3?
a.
4
b.
1
c.
2
d.
3


Solution:

d3ydt3 + tdydt+t2y =t3
[Write the differential equation.]

So, the order of the differential equation is 3
[The highest order derivative is the order of the differential equation.]


Correct answer : (5)
 7.  
Find the order of the differential equation (dydx)3 + d2ydx2 = 4y.
a.
1
b.
2
c.
3
d.
4


Solution:

(dydx)3 + d2ydx2 = 4y
[Write the differential equation.]

So, the order of the differential equation is 2
[The highest order derivative is the order of the differential equation.]


Correct answer : (3)
 8.  
What is the degree of the differential equation (dydx+d3ydx3)23 = 2y?
a.
4
b.
1
c.
3
d.
2


Solution:

(dydx+d3ydx3)23 = 2y
[Write the equation.]

(dydx+d3ydx3)2 = 8y3
[Cubing on both sides.]

(dydx)2 + 2(dydx)(d3ydx3) + (d3ydx3)2 = 8y3
[The degree of the differential equation is the highest exponent of the highest order derivative in it.]

So, the degree of the differential equation is 2


Correct answer : (5)
 9.  
What is the order of the differential equation y ′ + 2y = sin x?
a.
4
b.
1
c.
3
d.
2


Solution:

y ′ + 2y = sin x
[Write the differential equation.]

The order of the differential equation is 1.
[The highest order derivative is the order of the differential equation.]


Correct answer : (3)
 10.  
What is the degree of the differential equation (y ′′′)2 + (y ′′)3 + (y ′)4 + y5 = 0?
a.
1
b.
2
c.
3
d.
4


Solution:

(y ′′′)2 + (y ′′)3 + (y ′)4 + y5 = 0
[Write the differential equation.]

The degree of the differential equation is 2
[The highest exponent of the highest order derivative in the differential equation is the degree of the differential equation.]


Correct answer : (2)

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