Free Printable Ordinary Differential Equations and Limits (G12)

1.

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

a)

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

b)

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

c)

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

d)

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

2.

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)

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

3.

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)

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

4.

Please find the answer to this limit: $\lim_{x\rightarrow\infty}\frac{x^2+\sin x}{x^2}$ =

a)

0

b)

1

c)

-1

d)

$\infty$

5.

Please find 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)

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

6.

Please find $\lim_{x\rightarrow0}\frac{2x+\tan3x}{\sin x}$

a)

0

b)

2

c)

5

d)

$\infty$

Ordinary Differential Equations and Limits (G12)

Total questions: 6

Worksheet time: 15mins

Similar Resources on Wayground