Free Printable Classification of differential equations

1.

Is the given differential equation linear or nonlinear?

\frac{dy}{dx}=\tan x+15x^2+e^x+\frac{1}{x}

a)

linear

b)

non linear

c)

not sure

2.

2. What is the type of the function?

$\frac{𝑑𝑦}{dt}=\frac{3𝑡^2}{y}$

a)

Linear Partial Differential Equation

b)

Linear Ordinary Differential Equation

c)

Nonlinear Partial Differential Equation

d)

Nonlinear Ordinary Differential Equation

3.

$\frac{dy}{dt}=\frac{4t}{y}$

Given that $y\left(0\right)=1$ .Thus, the equation is

a)

an initial value problem

b)

a boundary value problem

4.

$\frac{dy}{dx}=\frac{x+1}{y+2}$

Is the equation homogeneous or nonhomogeneous?

a)

Homogeneous

b)

Nonhomogeneous

c)

Not sure

5.

$2\frac{d^2y}{dt^2}+\frac{dy}{dt}-\sin y=t^2$

This equation is second order, first degree, nonhomogeneous and nonlinear. Is it TRUE or FALSE?

a)

TRUE

b)

FALSE

c)

NOT SURE

6.

$\left(\frac{d^2u}{dt^2}\right)^2+\left(\frac{du}{dt}\right)^3+u=t$

State the order and degree of the following function

a)

Second order, second degree

b)

Second order, third degree

c)

First order, second degree

d)

First order, third degree

7.

$\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=2xy$

Tick the right boxes.

a)

Linear

b)

Nonlinear

c)

PDE

d)

ODE

8.

$\frac{\partial u}{\partial t}=\frac{\partial u}{\ \partial x}+\frac{\partial u}{\partial y}$

Write the independent variable(s) of this differential equation.

(a)

9.

$\frac{dy}{dt}+y=e^t$ .
Determine whether the equation is linear or nonlinear.

a)

Linear

b)

Nonlinear

c)

Not sure

10.

$\frac{\partial^2f}{\partial x^2}+\frac{\partial^2f}{\partial y^2}=0$

The solution to the differential equation is

a)

$f\left(x,t\right)$

b)

$f\left(x,y\right)$

c)

$y\left(f,x\right)$

d)

$x=f\left(y,t\right)$

11.

The differential equation is an equation contains of unknown ________ and its _____________

(a)

12.

The differential equations are useful to describe anything that changes in time or in space.

Is this statement TRUE or FALSE

a)

TRUE

b)

FALSE

c)

NOT SURE

13.

Which of the following differential equations has degree 2 and order 4?

a)

$\frac{d^4y}{dx^4}+2\ \frac{dy}{dx}+y=x$

b)

$\left(\frac{d^4y}{dt^{4\ }}\right)^2-3\ \frac{d^2y}{dt^{2\ }}+y=e^t$

c)

$\left(\frac{d^2y}{dt^2}\right)^4-\frac{dy}{dt}+3y=0$

d)

$\frac{d^2y}{dx^2}+\left(\frac{dy}{dx}\right)^4-5y=\sin x$

14.

Which one of the following differential equations is linear?

a)

$x\ \frac{d^2y}{dx^2}+\frac{dy}{dx}+3y=e^{2x}$

b)

$\frac{d^2y}{dx}-\frac{dy}{dx}+\sin y=0$

c)

$3\ \frac{d^2y}{dx^2}+\left(\frac{dy}{dx}\right)^2-y=\cos x$

d)

$2y\ \frac{d^2y}{dx^2}+4\ \frac{dy}{dx}+xy=5$

15.

Which of the following equations is partial differential equation?

a)

$\frac{dy}{dt}+y=e^t$

b)

$\frac{d^2y}{ds^2}+\frac{dy}{ds}+y=2s$

c)

$u_{xx}+u_t=0$

d)

$P_{tt}+P_t=t^2$

Classification of differential equations

Total questions: 15

Worksheet time: 15mins

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