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Linear Differential Equations

Which of following is a linear differential equation?

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

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

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

Which method is commonly used to solve linear differential equations?

Euler's method

Variation of parameters

Laplace transforms

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

True

False

Which of following is not a linear differential equation?

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

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

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

Which of following is a linear differential equation?

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

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

$y=x^2$

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

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

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

x

y

z

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

Linear

non-linear

none

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

True

False

Questions

Time

Score

Linear Differential Equations

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

Which method is commonly used to solve linear differential equations?

Euler's method

Variation of parameters

Laplace transforms

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

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

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

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

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

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

x

y

z

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

Linear

non-linear

none

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

True

False

Incorrect

Great!

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

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

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

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

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

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

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

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

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

$y=x^2$

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

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

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