# 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.

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

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.

4.
What is the degree of the differential equation ($\frac{{d}^{2}y}{{dx}^{2}}$)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.]

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

6.
What is the order of the differential equation $\frac{{d}^{3}y}{d{t}^{3}}$ + $t$$\frac{dy}{dt}+{t}^{2}y$ = $t$3?
 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.]

7.
Find the order of the differential equation ($\frac{dy}{dx}$)3 + $\frac{{d}^{2}y}{d{x}^{2}}$ = 4$y$.
 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.]

8.
What is the degree of the differential equation ${\left(\frac{dy}{dx}+\frac{{d}^{3}y}{d{x}^{3}}\right)}^{\frac{2}{3}}$ = 2$y$?
 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

9.
What is the order of the differential equation $y$ ′ + 2$y$ = 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.]

10.
What is the degree of the differential equation ($y$ ′′′)2 + ($y$ ′′)3 + ($y$ ′)4 + $y$5 = 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.]