Differential Equations Concepts and Solutions

Differential Equations Concepts and Solutions

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

Created by

Lucas Foster

FREE Resource

This video tutorial explains how to solve a second order homogeneous Cauchy-Euler differential equation. It begins by identifying the equation's form and coefficients, then uses the auxiliary equation to find the general solution. The process involves factoring a quadratic equation to determine the roots, which dictate the form of the general solution. The tutorial covers different cases for root types, including real equal roots, and concludes with a summary of the key points.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What type of differential equation is being solved in the video?

First order non-linear

Third order non-homogeneous

Second order homogeneous

First order linear

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of coefficient 'a' in the given differential equation?

2

4

0

1

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which term is missing in the given differential equation, making b equal to zero?

y''

y'

x

y

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving the auxiliary equation?

Factoring the equation

Finding the roots

Simplifying the equation

Substituting values of a, b, and c

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the nature of the roots found in the auxiliary equation?

Two real equal roots

Two distinct real roots

Two complex roots

One real and one complex root

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How does the presence of two real equal roots affect the general solution?

It includes a natural log term

It includes a polynomial term

It includes a sine and cosine term

It includes an exponential term

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What additional factor is included in the second term of the general solution for equal roots?

Natural log of x

Sine function

Exponential function

Cosine function

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