Free Printable DIFFERENTIAL QUIZ (BASIC 1)

1.

What is the order and degree for the differential equation: $\left(\frac{\text{d}y}{\text{d}x}\right)^4-\left(\frac{\text{d}^2y}{\text{d}x^2}\right)=-y$

a)

Order: 4
Degree: 1

b)

Order: 2
Degree: 1

c)

Order: 1
Degree: 4

d)

Order: 2
Degree: 4

2.

State the order and degree for differential equation below: $\left(\frac{\text{d}^2y}{\text{d}x^2}\right)^3+5\left(\frac{\text{d}y}{\text{d}x}\right)^4=\cos3x$

a)

Order:2
Degree: 4

b)

Order:3
Degree: 2

c)

Order:2
Degree: 3

d)

Order:4
Degree: 2

3.

Form the differential equation of the curve $y=5x^2+5A$

a)

$\frac{\text{d}y}{\text{d}x}=10x+5$

b)

$\frac{\text{d}y}{\text{d}x}=-10x$

c)

$\frac{\text{d}y}{\text{d}x}-10x=0$

d)

$\frac{\text{d}y}{\text{d}x}-10x=5$

4.

Form the differential equation of the curve:
$y=Ae^x+Be^{-x}$

a)

$\frac{\text{d}^2y}{\text{d}x^2}=y$

b)

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

c)

$\frac{\text{d}^2y}{\text{d}x^2}=Ae^x-Be^{-x}$

d)

$\frac{\text{d}^2y}{\text{d}x^2}=Axe^x-Bxe^{-x}$

5.

Solve the differential equation by using Direct Integration Method:
$\frac{\text{d}y}{\text{d}x}=4x^3-3x^2+1$

a)

$y=x^4-x^3+c$

b)

$y=3x^4-2x^3+x+c$

c)

$y=12x^3-6x^2$

d)

$y=x^4-x^3+x+c$

6.

Solve the first order differential equation by using Direct Integration Method:
$\frac{\text{d}y}{\text{d}x}=2x^3-6x$

a)

$y=6x^2-6+c$

b)

$y=\frac{x^4}{2}-3x^2+c$

c)

$y=\frac{3x^4}{2}-3x^2+c$

d)

$y=\frac{x^4}{2}-6x^2+c$

7.

Solve the first order differential equation by using Direct Integration Method:
$x\frac{\text{d}y}{\text{d}x}=4x^4+4$

a)

$y=x^4+4\ln x+c$

b)

$y=x^4+4x+c$

c)

$y=x^4+\ln4x+c$

d)

$y=x^4+4\ln4x+c$

8.

Solve the differential equation by using separable variable method.
$\frac{\text{d}y}{\text{d}x}=3x^2y$

a)

$\ln y=6x^2+c$

b)

$\ln y=2x^3+c$

c)

$\ln y=x^3+2y+c$

d)

$\ln y=x^3+c$

9.

Solve the differential equation by using separable variable method.
$y\frac{\text{d}y}{\text{d}x}=\frac{x^3}{y}$

a)

$\frac{y^2}{2}=\frac{x^4}{4}+c$

b)

$\frac{2y^3}{3}=\frac{x^4}{4}+c$

c)

$y^3=x^4+c$

d)

$\frac{y^3}{3}=\frac{x^4}{4}+c$

10.

Solve the differential equation by using separable variable method.
$\frac{5}{x}dy=3xy^2dx$

a)

$\frac{5}{y}=x^3+c$

b)

$\frac{-5}{y}=x^2+c$

c)

$\frac{-5}{y}=x^3+c$

d)

$\frac{5}{y}=2x^2+c$

DIFFERENTIAL QUIZ (BASIC 1)

Total questions: 10

Worksheet time: 18mins

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