Free Printable FIVIZZ: WEEK 18 - ADVANCED MATHEMATICS 2

1.

$\frac{\text{d}y}{\text{d}x}+y\ \cot\ x=\csc\ x$

Consider the Linear differential equation above. Choose the correct information about the differential equation above.

1. The integrating factor is sin x.
2. The general solution can be written as y sin x = x + A where A is a constant.
3. The general solution can be written as y sin x = C where C is a constant.
4.The integrating factor is cot x.

a)

1 and 2

b)

1 and 3

c)

2 and 4

d)

3 and 4

2.

The following is a Linearly Dependent Non-Homogeneous Differential Equation.

(x - 5y + 27)dx + (8x - 4y +36)dy = 0

a)

True

b)

False

3.

The particular solution of Exact differential equation, (2xy - sin x)dx + (x^2 - cos y)dy = 0, when y(0) = 0 is yx^2 + cos x - sin y = 1.

a)

True

b)

False

4.

$\left(2xy^2-3y^2+3y+3x\right)dx+\left(2yx^2-6xy+3x+2y\right)dy=0$ Equation above is an Exact Differential Equation.

a)

True

b)

False

5.

The particular solution of Exact differential equation, e^y dx + (2y + xe^y)dy = 0, when y(1) = 0 is xe^y + y^2 = -1.

a)

True

b)

False

6.

The particular solution of Exact Differential Equation, (6x^2 - y + 3)dx + (3y^2 - x -2)dy = 0, when y(1) = 0 is 2x^3 - xy +3x + y^3 - 2y = 5.

a)

True

b)

False

7.

$y^2dx+\left(yx-x^3\right)dy=0$

Equation above is a Linear Differential Equation.

a)

True

b)

False

8.

$\frac{1}{y}\frac{\text{d}y}{\text{d}x}=\frac{1}{y}\frac{e^x}{x^2}-\left(\frac{x+2}{x}\right)$

What is the integrating factor for linear differential equation above?

a)

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

b)

$x^2e^x$

c)

$1+\frac{2}{x}$

d)

$\frac{1}{1+x}$

9.

$xydy=dy-\frac{\left(1+y^2\right)}{2}dx$

What is the integrating factor for the linear differential equation above?

a)

$\frac{2}{1+y^2}$

b)

$\frac{y^2}{2xy-2}$

c)

$\frac{1}{2xy-2}$

d)

$1+y^2$

10.

$\left(1-x\right)dy=\left(x-y-x^3\right)dx$

What is the integrating factor for the linear differential equation above?

a)

$x\left(1-x\right)$

b)

$\frac{x-x^3}{1-x}$

c)

$1-x$

d)

$\frac{1}{1-x}$

FIVIZZ: WEEK 18 - ADVANCED MATHEMATICS 2

Total questions: 10

Worksheet time: 20mins

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