Free Printable First Order Ordinary Differential Equations

1.

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)

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

2.

Which of the following statement is TRUE.

a)

$\frac{\text{d}x}{\text{d}y}-\frac{2}{x}=e^x$ is linear and its integrating factor is $-\frac{1}{x^2}.$

b)

$\frac{\text{d}x}{\text{d}y}-4x=0\$ with condition $y\left(1\right)=2$ is linear and its solution is $y=2x^2.$

c)

$\frac{\text{d}x}{\text{d}y}-\frac{2}{x}=e^x\$ is linear and its solution is $y=\frac{1}{x^2}.$

d)

$y^3dx-4x^2dy=0$ is not exact.

3.

$\frac{\text{d}x}{\text{d}y}-4y-5+e^{-2x}=0$

The general solution for the above DE is,

a)

$y=-20+6e^{-2x}+Ce^{4x}$

b)

$y=-\frac{5}{4}e^{-4x}+\frac{1}{6}e^{-2x}+Ce^{4x}$

c)

$y=-20e^{-8x}+e^{-10x}+Ce^{-4x}$

d)

$y=-\frac{5}{4}+\frac{1}{6}e^{-2x}+Ce^{-4x}$

4.

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)

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

5.

Solve the given differential equations by separable variable method $\frac{\text{d}v}{\text{d}t}=\frac{3+v^2}{v}$

a)

$v=\ln\left|3+v^2\right|+C$

b)

$v^2=e^{2t+2c}-3$

c)

$v=Ae^{2t}+3,\ \ \ \ \ A=e^{2c}$

d)

$v^2=Ae^{2t}+3,\ \ \ \ \ \ A=C$

6.

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

a)

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

b)

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

c)

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

d)

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

7.

What is the order and degree of the differential equation?

a)

1, 2

b)

2, 1

c)

3, 2

d)

2, 3

8.

Determine the value of "c" that satisfies the differential equation $\frac{dy}{dx}=\frac{x+1}{y+2}$ if the curve goes through the point (0, -1).

a)

5/2

b)

-3/2

c)

-1/2

d)

1

9.

Solve the following differential equations:
$\frac{\text{d}y}{\text{d}x}=\frac{1}{\cos y}$

a)

$\sin y=1+C$

b)

$\sin y=x+C$

c)

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

d)

$\sin y=0+C$

10.

Solve the differential equation $\frac{dy}{dt}=\frac{3t^2}{y}$ with initial condition 𝑦(2) = 0.

a)

𝑦 = ln(15t)

b)

𝑦 = 16t³

c)

𝑦 = (2𝑡³− 16)^1/2

d)

𝑦 = (2𝑡³−16)

First Order Ordinary Differential Equations

Total questions: 10

Worksheet time: 30mins

Similar Resources on Wayground