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 |

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 |

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 |

Correct answer : (2)

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 |

[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

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 |

Correct answer : (4)

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 |

[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 ($\frac{dy}{dx}$)^{3} + $\frac{{d}^{2}y}{d{x}^{2}}$ = 4$y$.

a. | 1 | ||

b. | 2 | ||

c. | 3 | ||

d. | 4 |

[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 ${(\frac{dy}{dx}+\frac{{d}^{3}y}{d{x}^{3}})}^{\frac{2}{3}}$ = 2$y$?

a. | 4 | ||

b. | 1 | ||

c. | 3 | ||

d. | 2 |

[Write the equation.]

[Cubing on both sides.]

[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 $y$ ′ + 2$y$ = sin $x$?

a. | 4 | ||

b. | 1 | ||

c. | 3 | ||

d. | 2 |

[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} + $y$^{5} = 0?

a. | 1 | ||

b. | 2 | ||

c. | 3 | ||

d. | 4 |

[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)