Quiz about DE AHHHA

Question 1

Which is the condition of linear ordinary differential equations?

Accepted Answer

all of the above

Answer

The dependent variable y and its derivatives occur to the first degree only

Answer

No products of y and/or any of its derivatives appear in the equation

Answer

No transcendental functions of y and/or its derivatives occur

Question 2

These are equations involving two or more independent variables.

Accepted Answer

Partial Differential Equations

Answer

Differential Function

Answer

Differential Equations

Answer

Ordinary Differential Equations

Question 3

Which is not a method for solving differential equations of order one?

Accepted Answer

Linear Exact DE

Answer

Separation of Variables

Answer

Homogeneous DE

Answer

Exact DE

Question 4

This equation contains only one independent variable and one or more of its derivatives with respect to the

variable.

Accepted Answer

Ordinary Differential Equation

Answer

Partial Differential Equation

Answer

First Ordered Differential Equation

Answer

Differential Equation

Question 5

It is a function or a set of functions free of derivatives or differentials expressing the functional relationship

between the dependent and independent variables.

Accepted Answer

Solution to a DE

Answer

General Solution

Answer

Differential Equation

Answer

Particular Solution

Question 6

What is separation of variables?

Accepted Answer

It's when you move the dependent variable to one side of the equation and the independent variable to the

other side of the equation.

Answer

It's when the variables are not connected together.

Answer

It's when you move all the variables to one side of the equation and keep your constants on the other side.

Answer

It's when one variable is in the numerator and the other variable in the denominator.

Question 7

The highest power of the highest ordered derivative.

Accepted Answer

Degree

Answer

Order

Answer

Type

Answer

Coefficient

Question 8

Involves functions and derivatives. It contains only one independent variable and one or more of its derivatives with respect to the variable.

Accepted Answer

ODE

Answer

PDE

Answer

DE

Answer

0DE

Question 9

The solution which contains arbitrary constants C

Accepted Answer

General Solution

Answer

Solution To DE

Answer

Differential Equation

Answer

Particular Solution

Question 10

Obtained from the general solution by assigning specific values to the arbitrary constants.

Accepted Answer

Particular Solution

Answer

Solution to a DE

Answer

General Solution

Answer

Differential Equation

Question 11

What type of equation is this? M(x,y)dx+N(x,y)=0

Accepted Answer

First Ordered DE

Answer

DE

Answer

Second Ordered DE

Answer

GS

Question 12

An equation is Homogeneous DE if?

Accepted Answer

the degrees of M(x,y) and N(x,y) is the same

Answer

M(x,y) and N(x,y) is not same

Answer

the degrees of M(x,y) and N(x,y) is not the same

Answer

M(x,y) and N(x,y) is the same

Question 13

Test for Exactness Formula?

Accepted Answer

$$\frac{\partial M\left(x,y\right)}{\partial y}=\frac{\partial N\left(x,y\right)}{\partial x}$$

Answer

$$\frac{\partial xM\left(x,y\right)}{\partial y}=\frac{\partial yN\left(x,y\right)}{\partial x}$$

Answer

$$\frac{\partial N\left(x,y\right)}{\partial y}=\frac{\partial M\left(x,y\right)}{\partial x}$$

Answer

$$\frac{\partial M\left(x,y\right)}{\partial x}=\frac{\partial N\left(x,y\right)}{\partial y}$$

Question 14

$$\frac{1}{N}\left(\frac{\partial M}{\partial y}-\frac{\partial N}{\partial x}\right)=f\left(x\right)$$ then what is the I.F.?

Accepted Answer

$$e^{\int f\left(x\right)dx_{ }^{ }}$$

Answer

$$e^{-\int f\left(x\right)dx_{ }^{ }}$$

Answer

$$e^{-\int f\left(y\right)dy_{ }^{ }}$$

Answer

$$e^{\int f\left(y\right)dy^{ }}$$

Question 15

$$\frac{1}{M}\left(\frac{\partial M}{\partial y}-\frac{\partial N}{\partial x}\right)=f\left(y\right)$$ then what is the I.F.?

Accepted Answer

$$e^{-\int f\left(y\right)dy_{ }^{ }}$$

Answer

$$e^{-\int f\left(x\right)dx_{ }^{ }}$$

Answer

$$e^{\int f\left(x\right)dx_{ }^{ }}$$

Answer

$$e^{\int f\left(y\right)dy^{ }}$$

Question 16

What is this equation? $$\frac{ ext{d}x}{ ext{d}y}+x\ P\left(y ight)\ =\ Q\left(y ight)$$

Accepted Answer

Standard Form of FOLDE

Answer

Ordinary Form of FOLDE

Answer

Second Order Linear Differential Equation

Answer

Integration Factor

Question 17

First Order Linear Differential Equation

Accepted Answer

$$\frac{ ext{d}y}{ ext{d}x}+y\ P\left(x ight)=Q\left(x ight)\ ;\ \phi\left(x ight)=e^{\int P\left(x ight)dx};\ y\phi\left(x ight)=\int Q\left(x ight)\phi\left(x ight)dx$$

Answer

$$\frac{ ext{d}y}{ ext{d}x}+y\ P\left(x ight)=Q\left(x ight)\ ;\ \phi\left(x ight)=e^{\int Q\left(x ight)dx};\ y\phi\left(x ight)=\int P\left(x ight)\phi\left(x ight)dx$$

Answer

$$\frac{ ext{d}x}{ ext{d}y}+y\ P\left(x ight)=Q\left(x ight)\ ;\ \phi\left(y ight)=e^{\int P\left(x ight)dx};\ y\phi\left(x ight)=\int Q\left(x ight)\phi\left(x ight)dx$$

Answer

$$\frac{ ext{d}y}{ ext{d}x}-y\ P\left(x ight)=Q\left(x ight)\ ;\ \phi\left(x ight)=e^{\int P\left(x ight)dx};\ y\phi\left(x ight)=\int Q\left(x ight)\phi\left(x ight)dx$$

Question 18

What topic do you need this Equation? $$\frac{1}{N}\left(\frac{\partial M}{\partial y}-\frac{\partial N}{\partial y}\right)=f\left(x\right)$$

Accepted Answer

NON EXACT DE

Answer

EXACT DE

Answer

Bernoulli DE

Answer

NON-HOMOGENEOUS DE

Question 19

Non-Linear DE that can be reduced to a linear one or the form of FOLDE by a clever substitution, which can be solved explicitly.

Accepted Answer

BERNOULLI DE

Answer

FOLDE

Answer

SEPARABLE DE

Answer

BERNOULI DE

Question 20

What is the formula needed to solve for Z in Bernoulli DE?

Accepted Answer

$$y^{\left(1-n\right)}$$

Answer

1-n

Answer

(1-n) P(x)

Answer

$$y^{\left(n-1\right)}$$

Question 21

What are the equations for reduced Form of P(x) and Q(x) in Bernoulli DE?

Accepted Answer

$$\Pr\left(x\right)=\left(1-n\right)\ P\left(x\right)\ and\ Qr\left(x\right)=\left(1-n\right)\ Q\left(x\right)$$

Answer

$$\Pr\left(x\right)=\left(1-n\right)\ Q\left(x\right)\ and\ Qr\left(x\right)=\left(1-n\right)\ P\left(x\right)$$

Answer

$$\Pr\left(x\right)=\left(n-1\right)\ P\left(x\right)\ and\ Qr\left(x\right)=\left(n-1\right)\ Q\left(x\right)$$

Answer

None of the choices

Question 22

If c is some constant and the initial value of the function, $$y=Ce^x$$ is six, determine the equation.

Accepted Answer

$$y=6e^x$$

Answer

y=0

Answer

$$y=e^x$$

Question 23

Solve the given differential equation by separation of variables.

$$x\frac{ ext{d}y}{ ext{d}x}=6y$$

Accepted Answer

$$y=Cx^6$$

Answer

$$y=x^6\ +C$$

Answer

$$y=x^6$$

Answer

None of the above

Question 24

Formula for Solving Bernoulli DE?

Accepted Answer

$$z\phi x=\int Q\left(r\right)\phi xdx$$

Answer

$$y\phi x=\int Q\left(x\right)\phi xdx$$

Answer

$$z\phi x=\int P\left(r\right)\phi xdx$$

Answer

$$z\phi y=\int Q\left(r\right)\phi xdy$$

Question 25

Formula for Coefficients Linear in Two Variable Parallel Lines Solution

Accepted Answer

$$\left(v+C1\right)dx+\left(kv+C2\right)dy=0$$

Answer

$$\left(v+C1\right)dx+\left(v+C2\right)dy=0$$

Answer

$$\left(v+C1\right)dx+\left(kv+C2\right)dy$$

Answer

$$\left(v+C\right)dx+\left(kv+C\right)dy=0$$

Question 26

Formula for Coefficients Linear in Two Variable Intersecting Lines Solution

Accepted Answer

$$\left(A_1u+B_1v\right)du+\left(A_2u+B_2v\right)dv=0$$

Answer

$$\left(A_1u+B_1v\right)du+\left(A_2u+B_2v\right)dv$$

Answer

$$\left(A_1u+B_1v\right)dv+\left(A_2u+B_2v\right)du=0$$

Answer

$$None\ of\ the\ choices$$

Question 27

In Intersecting Lines Formula, x=? and y=?

Accepted Answer

x= u + h ; y =v+k

Answer

x= u + k ; y =v+h

Answer

x= k ; y= h

Answer

x= v+h ; y =u+k

Question 28

Formula for Growth and Decay

Accepted Answer

$$x=Ce^{kt}$$

Answer

$$x=Ce^{-kt}$$

Answer

$$x=e^{kt}+C$$

Answer

None of the Choices

Question 29

Formula for Newton's Law of Cooling

Accepted Answer

$$T-T_s=Ce^{-kt}$$

Answer

$$T-T_s=Ce^{kt}$$

Answer

$$T=Ce^{-kt}-T_s$$

Answer

None of the Choices

Question 30

Which of the following is not a Formula for Mixing Problems

Accepted Answer

$$C_{out\ }=\frac{Q_{out}}{R_{out}}$$

Answer

$$V\left(t\right)=V\left(0\right)=R_{in\ }\left(t\right)-R_{out}\left(t\right)$$

Answer

$$\frac{ ext{d}Q\left(t ight)}{ ext{d}t}=R_{in}C_{in}-R_{out}C_{out}$$

Answer

$$C_{out}=\frac{Q\left(t\right)}{V\left(t\right)}$$

Question 31

$$\frac{ ext{d}Q\left(t ight)}{ ext{d}t}=R_{in}C_{in}-R_{out}C_{out}$$ what is $$R_{in}C_{in}$$ ?

Accepted Answer

Rate and Concentration at which Q(t) enter the tank

Answer

Rate and Concentration at which Q(t) exits the tank

Answer

Rate and Concentration at which Q(t) dissolves the tank

Answer

Rate and Concentration at which Q(t) mixed in the tank

Question 32

$$T-T_s=Ce^{-kt}$$ what is Ts?

Accepted Answer

Ambient Temperature

Answer

Temperature of the medium

Answer

Temperature of the body

Answer

Object Temperature at any time

Question 33

$$x=Ce^{kt}$$ what is x

Accepted Answer

Measuring something positive

Answer

Time

Answer

Amount either positive or negative

Answer

Measuring something negative

Question 34

$$i=\frac{E}{R}\left[1-e^{\left(\frac{R}{L}\right)t}\right]$$ is the right formula for Series RL Circuit

Accepted Answer

Forda wrong

Accepted Answer

Fault

Answer

TRU

Answer

Pak

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