Quiz about Second Order Linear DE

Question 1

Standard form for 2nd order linear DE is

Accepted Answer

$$ay$$

Answer

$$y$$

Answer

$$y$$

Question 2

A 2nd order linear DE $$ay$$ is homogeneous if

Accepted Answer

$$Q=0$$

Answer

$$a=0$$

Answer

$$b=0$$

Answer

$$c=0$$

Question 3

A 2nd order linear DE $$ay$$ has a general solution of the form

Accepted Answer

$$y=y_c+y_p$$

Answer

$$y=C_1e^{\alpha x}+C_2e^{\beta x}$$

Answer

$$Iy=\int IQ\ dx$$

Answer

$$y=\left(C_1+C_2x\right)e^{\alpha x}$$

Question 4

To find the complementary function $$y_c$$ of the general solution of $$ay$$ we use characteristic equation

Accepted Answer

$$am^2+bm+c=0$$

Answer

$$am^2+bm+c=Q$$

Answer

$$m^2+bm+c=0$$

Answer

$$am^2+bm=c$$

Question 5

A 2nd order linear DE $$ay$$ can be written in the D-operator form as

Accepted Answer

$$aD^2y+bDy+cy=Q$$

Answer

$$aD^2+bD+c=Q$$

Answer

$$aD^2y+bDy+cy=0^{ }$$

Answer

$$aD^2y+bDy+c=Q$$

Question 6

The D-operator $$Dy$$ is equivalent to

Accepted Answer

$$\frac{dy}{dx}$$

Accepted Answer

$$y$$

Answer

$$\frac{d^2y}{dx^2}$$

Question 7

The D-operator $$D^2y$$ is equivalent to

Accepted Answer

$$\frac{d^2y}{dx^2}$$

Accepted Answer

$$y$$

Answer

$$\frac{dy}{dx}$$

Question 8

To find the particular function $$y_p$$ of the general solution of $$ay$$ we use inverse D-operator

Accepted Answer

$$y_p=\frac{1}{aD^2+bD+c}\left(Q\right)$$

Answer

$$y_p=\left(aD^2+bD+c\right)\left(Q\right)$$

Answer

$$y_p=\frac{1}{D}\left(Q\right)$$

Answer

$$y_p=\frac{1}{aD^2+bD+c}\left(0\right)$$

Question 9

The particular function $$y_p$$ of $$y$$ is

Accepted Answer

$$y_p=\frac{1}{D^2+2D+1}\left(5\right)$$

Answer

$$y_p=\left(D^2+2D+1\right)\left(5\right)$$

Answer

$$y_p=\frac{1}{D}\left(5\right)$$

Answer

$$y_p=\frac{1}{D^2+2D}\left(5\right)$$

Question 10

The inverse D-operator $$\frac{1}{D}\left[f\left(x\right)\right]$$ is equivalent to

Accepted Answer

$$\int f\left(x\right)\ dx$$

Answer

$$\frac{d}{dx}\left(f\left(x\right)\right)$$

Answer

$$f$$

Answer

$$\int f$$

Second Order Linear DE

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics