|BSM

Questions

1 / 10

Time

Score

Linear Differential Equations

Is the sentence true or false?
A linear differential equation with constant coefficients can be solved using the method of characteristic roots

True

False

Is the sentence true or false?
In a linear differential equation, if the coefficients P(x) and Q(x) are functions of the dependent variable y, the equation is considered non-linear

True

False

Which of following is not a linear differential equation?

$\frac{dy}{dx}=\ln y$

$\frac{dy}{dx}=e^{3x}$

$\frac{dy}{dx}=\cos\cos x+y$

Fill in the blank:
The equation (dy/dx) + 7y = e^x , is called _________ differential equation

Linear

non-linear

none

Which of following is a linear differential equation?

$\frac{dy}{dx}+x=\cos y$

$\frac{dy}{dx}+xy=\cos y$

$y=x^2$

Which method is commonly used to solve linear differential equations?

Euler's method

Variation of parameters

Laplace transforms

What is the defining characteristic of a linear differential equation?

The highest power of the dependent variable is 2

The dependent variable is raised to different powers

The equation involves linear combinations of the dependent variable and its derivatives

Is the sentence true or false?
The given equation a (dy/dx) + xy = y, is a linear differential equation

True

False

In a linear differential equation (dy/dx) + Py = Q, P(x) and Q(x) are functions of the dependent variable:

x

y

z

Which of following is a linear differential equation?

$\frac{dy}{dx}=y^2$

$\frac{dy}{dx}=e^{3y}$

$\frac{dy}{dx}=\cos\cos x+y$

Questions

Time

Score

Linear Differential Equations

Is the sentence true or false?A linear differential equation with constant coefficients can be solved using the method of characteristic roots

True

False

Is the sentence true or false? In a linear differential equation, if the coefficients P(x) and Q(x) are functions of the dependent variable y, the equation is considered non-linear

True

False

Which of following is not a linear differential equation?

﻿dydx=ln⁡y\frac{dy}{dx}=\ln ydxdy​=lny﻿

﻿﻿dydx=e3x\frac{dy}{dx}=e^{3x}dxdy​=e3x﻿

﻿dydx=cos⁡cos⁡x+y\frac{dy}{dx}=\cos\cos x+ydxdy​=coscosx+y﻿

Fill in the blank:The equation (dy/dx) + 7y = ex , is called _________ differential equation

Linear

non-linear

none

Which of following is a linear differential equation?

﻿dydx+x=cos⁡y\frac{dy}{dx}+x=\cos ydxdy​+x=cosy﻿

﻿dydx+xy=cos⁡y\frac{dy}{dx}+xy=\cos ydxdy​+xy=cosy﻿

﻿﻿y=x2y=x^2y=x2﻿

Which method is commonly used to solve linear differential equations?

Euler's method

Variation of parameters

Laplace transforms

What is the defining characteristic of a linear differential equation?

The highest power of the dependent variable is 2

The dependent variable is raised to different powers

The equation involves linear combinations of the dependent variable and its derivatives

Is the sentence true or false? The given equation a (dy/dx) + xy = y, is a linear differential equation

True

False

In a linear differential equation (dy/dx) + Py = Q, P(x) and Q(x) are functions of the dependent variable:

x

y

z

Which of following is a linear differential equation?

﻿dydx=y2\frac{dy}{dx}=y^2dxdy​=y2﻿

﻿dydx=e3y\frac{dy}{dx}=e^{3y}dxdy​=e3y﻿

﻿dydx=cos⁡cos⁡x+y\frac{dy}{dx}=\cos\cos x+ydxdy​=coscosx+y﻿

Incorrect

Great!

Is the sentence true or false?
A linear differential equation with constant coefficients can be solved using the method of characteristic roots

Is the sentence true or false?
In a linear differential equation, if the coefficients P(x) and Q(x) are functions of the dependent variable y, the equation is considered non-linear

$\frac{dy}{dx}=\ln y$

$\frac{dy}{dx}=e^{3x}$

$\frac{dy}{dx}=\cos\cos x+y$

Fill in the blank:
The equation (dy/dx) + 7y = e^x , is called _________ differential equation

$\frac{dy}{dx}+x=\cos y$

$\frac{dy}{dx}+xy=\cos y$

$y=x^2$

Is the sentence true or false?
The given equation a (dy/dx) + xy = y, is a linear differential equation

$\frac{dy}{dx}=y^2$

$\frac{dy}{dx}=e^{3y}$

$\frac{dy}{dx}=\cos\cos x+y$