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Ordinary Differential Equations

Is the sentence true or false?
A second-order ODE can be reduced to two first-order ODEs

True

False

Which of following is example of ODE?

$x^4y+x^2=0$

$\frac{\alpha^2u}{\alpha x^2}-\frac{\alpha^2u}{\alpha y^2}=0$

$\frac{1}{7}\ \frac{dy}{dx}=x+1$

Fill in the blank:
The equation (x+y)²dy =xydx is an example of

ODE

PDE

OED

Which of following is example of ODE?

$x^4y+x^2=0$

$\left(4yx^2\right)dx+\left(xy\right)dy=0$

$xy^3+x^3y=1$

Which of following is not ODE?

$x^4y+x^2y^{'''}=0$

$\frac{\alpha^2u}{\alpha x^2}-\frac{\alpha^2u}{\alpha y^2}=0$

$\frac{dy}{dx}=9$

Fill in the blank
The equation xy^’’=tantanx, is an _________ differential equation

non-linear

exact

ordinary

Is the sentence true or false?
An ODE that is not of the form dy/dx is not considered a first-order ODE

True

False

An ODE that can be separated into two equations, one involving only x and the other involving only y, is called a

Linear ODE

Exact ODE

Separable ODE

Which of following is example of ODE?

$xy+x^3=0$

$xy^2+x^3=0$

xy^''+x³y^'=10

Fill in the blank:
________is an equation that contains only one independent variable and one or more of its derivatives with respect to the variable

OED

ODE

EDO

Questions

Time

Score

Ordinary Differential Equations

Is the sentence true or false?A second-order ODE can be reduced to two first-order ODEs

True

False

Which of following is example of ODE?

﻿x4y+x2=0x^4y+x^2=0x4y+x2=0﻿

﻿α2uαx2−α2uαy2=0\frac{\alpha^2u}{\alpha x^2}-\frac{\alpha^2u}{\alpha y^2}=0αx2α2u​−αy2α2u​=0﻿

﻿17 dydx=x+1\frac{1}{7}\ \frac{dy}{dx}=x+171​ dxdy​=x+1﻿

Fill in the blank:The equation (x+y)2 dy =xydx is an example of

ODE

PDE

OED

Which of following is example of ODE?

﻿x4y+x2=0x^4y+x^2=0x4y+x2=0﻿

﻿(4yx2)dx+(xy)dy=0\left(4yx^2\right)dx+\left(xy\right)dy=0(4yx2)dx+(xy)dy=0﻿

﻿xy3+x3y=1xy^3+x^3y=1xy3+x3y=1﻿

Which of following is not ODE?

﻿x4y+x2y′′′=0x^4y+x^2y^{'''}=0x4y+x2y′′′=0﻿

﻿α2uαx2−α2uαy2=0\frac{\alpha^2u}{\alpha x^2}-\frac{\alpha^2u}{\alpha y^2}=0αx2α2u​−αy2α2u​=0﻿

﻿dydx=9\frac{dy}{dx}=9dxdy​=9﻿

Fill in the blankThe equation xy’’=tantanx, is an _________ differential equation

non-linear

exact

ordinary

Is the sentence true or false?An ODE that is not of the form dy/dx is not considered a first-order ODE

True

False

An ODE that can be separated into two equations, one involving only x and the other involving only y, is called a

Linear ODE

Exact ODE

Separable ODE

Which of following is example of ODE?

﻿xy+x3=0xy+x^3=0xy+x3=0﻿

﻿xy2+x3=0xy^2+x^3=0xy2+x3=0﻿

xy''+x3y'=10

Fill in the blank:________is an equation that contains only one independent variable and one or more of its derivatives with respect to the variable

OED

ODE

EDO

Incorrect

Great!

Is the sentence true or false?
A second-order ODE can be reduced to two first-order ODEs

$x^4y+x^2=0$

$\frac{\alpha^2u}{\alpha x^2}-\frac{\alpha^2u}{\alpha y^2}=0$

$\frac{1}{7}\ \frac{dy}{dx}=x+1$

Fill in the blank:
The equation (x+y)²dy =xydx is an example of

$x^4y+x^2=0$

$\left(4yx^2\right)dx+\left(xy\right)dy=0$

$xy^3+x^3y=1$

$x^4y+x^2y^{'''}=0$

$\frac{\alpha^2u}{\alpha x^2}-\frac{\alpha^2u}{\alpha y^2}=0$

$\frac{dy}{dx}=9$

Fill in the blank
The equation xy^’’=tantanx, is an _________ differential equation

Is the sentence true or false?
An ODE that is not of the form dy/dx is not considered a first-order ODE

$xy+x^3=0$

$xy^2+x^3=0$

xy^''+x³y^'=10

Fill in the blank:
________is an equation that contains only one independent variable and one or more of its derivatives with respect to the variable