Free Printable T-ENGM220 Diagnostic Exam

1.

Which of the following is the solution to the differential equation $\frac{dy}{dx}=\frac{x^2}{y}$ with the initial condition y(3) = -2?

a)

$y=-2e^{\left(-9+\frac{x^3}{3}\right)}$

b)

$y=\sqrt{\frac{2x^3}{3}}$

c)

$y=\sqrt{\frac{2x^3}{3}-14}$

d)

$y=-\sqrt{\frac{2x^3}{3}-14}$

2.

Given the differential equation dP/Dt=5P

A) Find the general solution for P to the differential equation

B)Find the particular solution for P to the differential equation given P(0)= 418

a)

A) P=Ce^5t

B) P= 5e^418t

b)

A) P=Ce^5t

B) P= 418e^5t

c)

A) P=Ce^t

B) P= 418e^t

d)

A) P=Ce^10t

B) P= 418e^10t

3.

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

a)

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

b)

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

c)

$x^2=y^2+C$

d)

$y^2=x^2+2C$

4.

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

a)

$y=Ax$

b)

$y^2=\ln x+C$

c)

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

d)

$A=yx$

5.

Degree of Differential equation is

a)

Power of highest order derivative

b)

Highest power

c)

Highest order derivative in DE

d)

None of above

6.

I.F. of $\frac{\text{d}x}{\text{d}y}+Px=Q$ is given by:

a)

$e^{\int Pdx_{ }}$

b)

$e^{\int Pdy_{ }}$

c)

$e^{\int Qdy_{ }}$

d)

$e^{\int Qdx_{ }}$

7.

The following Differential Equation is
$\frac{\text{d}y}{\text{d}x}=x^2y+x$

a)

Separable.

b)

Non Separable.

8.

What is DE

a)

Contains variables

b)

Have constants

c)

Contains variables and its derivatives

d)

Has image

9.

What do mean by linear

a)

Degree 1

b)

Degree 2

c)

Degree 3

d)

Degree 4

10.

What is homogeneous

a)

same degree

b)

same order

c)

different degree

d)

different order

11.

The population of the little town of Scorpion Gulch is now 1000 people. The population is presently growing at about 5% per year.

Find the general solution.

a)

P=.05e^1000t

b)

P=1000e^5t

c)

P=1000e^.05t

d)

p=lne^1000t

12.

Which of the following is the solution to the differential equation dy/dx=(x^2)/y with initial condition y(3)=-2?

a)

$y=2e^{\frac{-9+x^3}{3}}$

b)

$y=-2e^{\frac{-9+x^3}{3}}$

c)

$y=\sqrt{\frac{2x^3}{3}}$

d)

$y=\sqrt{\frac{2x^3}{3}-14}$

e)

$y=-\sqrt{\frac{2x^3}{3}-14}$

13.

What is the general solution to the DE $\frac{\text{d}^2x}{\text{d}y^2}+7\frac{\text{d}x}{\text{d}y}-8y=0$ ?

a)

$y=Ce^{-x}+De^{8x}$

b)

$y=Ce^x+De^{-8x}$

c)

$y=Ce^x+De^{7x}$

d)

$y=Ce^{-x}+De^{7x}$

14.

$\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)

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

15.

Given $\frac{\text{d}^2x}{\text{d}y^2}+4\frac{\text{d}x}{\text{d}y}+3y=2e^{-x}.$

The correct $y_p$ is

a)

$Ce^{-x}$

b)

$C\cos x+D\sin x$

c)

$Ce^x$

d)

$Cxe^{-x}$

16.

What is the integrating factor for the differential equation: $\frac{1}{x}\frac{\text{d}x}{\text{d}y}-\frac{1}{1+x^2}y=x^3$

a)

$\ln\left(x^2\right)$

b)

$-\frac{1}{x^2}$

c)

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

d)

$\frac{1}{\sqrt{x}}$

17.

The solution of linear differential equation $x\frac{\text{d}y}{\text{d}x}+2y=x^2$

a)

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

b)

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

c)

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

d)

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

18.

Which of the following mathematical models CANNOT be solved by using separation of variables

a)

$\frac{\text{d}P}{\text{dt}}=kP$

b)

$\frac{dT}{dt}=k\left(T-Tm\right)$

c)

$\frac{dA}{dt}=kA$

d)

$L\ \frac{dI}{dt}+RI=E\left(t\right)$

19.

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

20.

Tick the following topic which are a real-life application of the concept of Differential Equations

a)

Population Growth

b)

Newton's Law of Cooling

c)

Acceleration-velocity

d)

Epidemic model

e)

Wind direction on a weather map

T-ENGM220 Diagnostic Exam

Total questions: 20

Worksheet time: 3600secs

Similar Resources on Wayground