Free Printable Differential Equation

1.

dy/dx = 4x/y. Suppose y(0)=1

The particular solution is

a)

B

b)

C

c)

D

d)

E

2.

The following Differential Equation is
$\frac{\text{d}y}{\text{d}x}=\frac{y}{x}$

a)

Separable.

b)

Non Separable

3.

Is this a Linear Differential equation

a)

Yes

b)

No

c)

Maybe

d)

red

4.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=e^x$

a)

$1=e^x+C$

b)

$y=\frac{e^x}{2}+C$

c)

$y=e^x+C$

d)

$0=e^x+C$

5.

Which functions below will have the same slope field? (choose all that apply)

a)

y = x² - 3

b)

y = x² + 4

c)

y = 2x - 5

d)

y = 2x²

6.

In drawing the slope field for the differential equation , I would place short slope lines of _________ at the points (0,1), (1,-1), and (2,-2)
$\frac{dy}{dx}=2x-3y$

Select all that apply

a)

-3

b)

-1

c)

2

d)

5

e)

10

7.

y is proportional to the product of z and the square root of x

a)

$y=zx^2$

b)

$y=kzx^2$

c)

$y=kz\sqrt{x}$

d)

$y=zkx$

8.

The degree of a differential equation is define by a

a)

Positive real number

b)

Positive rational number

c)

Positive integer

d)

All the above

9.

Solution of a linear differential equation of first order can be obtain by

a)

multiplying on both the sides by its integrating factor.

b)

adding on both the sides by integrating factor.

c)

subtracting integrating factor from both sides

d)

None of the above

10.

The complete solution of Linear Differential equations involves

a)

complete function + particular integral

b)

complementary function + particular integral

c)

complementary function + definite integral

d)

complete function + indefinite integral

11.

The particular integral of the equation $\left(D-1\right)y=e^{3x}$ is

a)

$\frac{e^{3x}}{2}$

b)

$\frac{e^{-3x}}{2}$

c)

$\frac{e^{3x}}{4}$

d)

$\frac{e^x}{2}$

12.

The C.F. of the equation $\left(D^2-9\right)y=e^{-3x}+1+e^{3x}$ is

a)

$c_1e^{-3x}+c_2e^{-x}$

b)

$c_1e^{3x}+c_2e^{3x}$

c)

$c_1e^{3x}+c_2e^{-x}$

d)

$c_1e^{3x}+c_2e^{-3x}$

13.

Choose the right description for the given differential equation

a)

Ordinary, 2nd order, degree 2, non linear

b)

Partial, 1st order, degree 2, linear.

c)

Ordinary, 1st order, degree 2, linear

d)

Partial, 2nd order, degree 1, non linear

14.

Number of arbitrary constant in the general solution of a differential equation of degree 3 and order 4 is

a)

3

b)

4

c)

0

d)

4³

15.

$\frac{\text{d}^2x}{\text{d}y^2}+6\frac{\text{d}x}{\text{d}y}-5y=0\$

The general solution to the DE is,

a)

$y=Ae^x+Be^{5x}$

b)

$y=Ae^{-x}+Be^{-5x}$

c)

$y=Ae^{\left(-3+\sqrt{14}\right)x}+Be^{\left(-3-\sqrt{14}\right)x}$

d)

$y=A\cos\left(-3+\sqrt{14}\right)x+B\sin\left(-3-\sqrt{14}\right)x$

16.

Find a solution for y if dy/dx = 2x√y and y = 4 when x = 3.

a)

2√y = x² + C

b)

y = (x² + 25)²/4

c)

y = x⁴/4

d)

y = ¼(x² - 5)²

17.

Which of the following equations solves dy/dt = ky?

a)

y = y₀e^kt

b)

y = mx + b

c)

y = a(x - h)² + k

d)

y = Asin[B(x - C)] + D

18.

What movie is this photo from?

a)

Oliver & Company

b)

Lion King

c)

Lady & the Tramp

d)

Jungle Book

19.

What movie is this picture from?

a)

Little Mermaid

b)

Lady & the Tramp

c)

Bugs Life

d)

Frozen

20.

2. Solve the differential equation

𝑑𝑦/𝑑𝑡 =3𝑡²/𝑦 with initial condition

𝑦(2) = 0.

a)

$y=\ln\left|15t\right|$

b)

$y=16t^3$

c)

$y\ =\ \sqrt{2t^3-16}$

d)

$y=2t^3-16$

Differential Equation

Total questions: 20

Worksheet time: 14mins

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