Free Printable Second Order Linear DE

1.

Standard form for 2nd order linear DE is

a)

$ay''+by'+cy=0$

b)

$ay''+by'+cy=Q$

c)

$y''+by'+cy=0$

d)

$y''+by'+cy=Q$

2.

A 2nd order linear DE $ay''+by'+cy=Q$ is homogeneous if

a)

$a=0$

b)

$b=0$

c)

$c=0$

d)

$Q=0$

3.

A 2nd order linear DE $ay''+by'+cy=Q$ has a general solution of the form

a)

$y=y_c+y_p$

b)

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

c)

$Iy=\int IQ\ dx$

d)

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

4.

To find the complementary function $y_c$ of the general solution of $ay''+by'+cy=Q$ we use characteristic equation

a)

$am^2+bm+c=Q$

b)

$am^2+bm+c=0$

c)

$m^2+bm+c=0$

d)

$am^2+bm=c$

5.

A 2nd order linear DE $ay''+by'+cy=Q$ can be written in the D-operator form as

a)

$aD^2+bD+c=Q$

b)

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

c)

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

d)

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

6.

The D-operator $Dy$ is equivalent to

a)

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

b)

$\frac{dy}{dx}$

c)

$y''$

d)

$y'$

7.

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

a)

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

b)

$\frac{dy}{dx}$

c)

$y''$

d)

$y'$

8.

To find the particular function $y_p$ of the general solution of $ay''+by'+cy=Q$ we use inverse D-operator

a)

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

b)

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

c)

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

d)

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

9.

The particular function $y_p$ of $y''+2y'+y=5$ is

a)

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

b)

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

c)

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

d)

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

10.

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

a)

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

b)

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

c)

$f'\left(x\right)$

d)

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

Second Order Linear DE

Total questions: 10

Worksheet time: 5mins

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