Free Printable Linear DE

1.

The standard form of 1st order linear ODE is

a)

$y'+Py=0$

b)

$ay'+by+c=0$

c)

$y'+Py=Q$

d)

$y'+by+c=0$

2.

Which of the following are 1st order linear ODE?

a)

$y'=y$

b)

$\frac{dy}{dx}-2y=5$

c)

$y'+\frac{y}{x}=x^2$

d)

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

3.

The first step in solving 1st order linear ODE is

a)

making sure it is of standard form

b)

making one side equals to zero

c)

identify P and Q

d)

compute the integrating factor

4.

The second step in solving 1st order linear ODE is

a)

making sure it is of standard form

b)

making one side equals to zero

c)

identify P and Q

d)

compute the integrating factor

5.

The third step in solving 1st order linear ODE is

a)

making sure it is of standard form

b)

making one side equals to zero

c)

identify P and Q

d)

compute the integrating factor

6.

The integrating factor of the linear DE $y'+\frac{y}{x}=x^2$ is

a)

$\int\frac{1}{x}dx$

b)

$e^{\left(\int\frac{1}{x}dx\right)}$

c)

$e^{\frac{1}{x}}$

d)

$e^{\left(\int x^2dx\right)}$

7.

The integrating factor $I=e^{\left(\int\frac{1}{x}dx\right)\ }$ can be simplified into

a)

$e^{\ln x}$

b)

$x$

c)

$\ln x$

d)

$e^x$

8.

The formula for the general solution of 1st order linear DE is

a)

$y=\int IQdx$

b)

$Iy=\int Qdx$

c)

$y=\int IQdx$

d)

$Iy=\int IQdx$

9.

The standard form for 2nd order linear DE is

a)

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

b)

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

c)

$y''+Py'=Q$

d)

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

10.

Which of the following is a homogeneous 2nd order linear DE?

a)

$y''-2y'=0$

b)

$y''-2y'+y=0$

c)

$y''+2y'=x$

d)

$y''-4y=e^x$

11.

The characteristic equation of the DE $y''-2y'+y=0$ is

a)

$m^2-2m=0$

b)

$m^2-2m=1$

c)

$m-2m+1=0$

d)

$m^2-2m+1=0$

12.

Which of the following are general solution of a homogeneous 2nd order DE?

a)

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

b)

$y=C\ e^{\left(\alpha+\beta\right)x}$

c)

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

d)

$y=e^{px}\left(C_1\sin\left(qx\right)+C_2\cos\left(qx\right)\right)$

Linear DE

Total questions: 12

Worksheet time: 12mins

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