Free Printable Partial Differential Equations

1.

A PDE consists of

a)

only one independent variable

b)

more than one independent variable

c)

more than one dependent varible

2.

The highest derivative in the given pde is called

a)

order

b)

degree

3.

The degree of the following pde $\left(\text{}\frac{\partial z}{\partial x}\ \right)^2+2\left(\frac{\partial^2z}{\partial x\partial y}\right)+\left(\frac{\partial z}{\partial y}\right)^2=0$ is

a)

2

b)

0

c)

1

4.

The order of the following pde $\left(z_{xx}\right)^2+\left(z_{xyy}\right)+\left(z_{yy}\right)=\sin z$ is

a)

1

b)

2

c)

3

5.

The expansion for s

a)

$\frac{\partial^2z}{\partial y^2}$

b)

$\frac{\partial^2z}{\partial x^2}$

c)

$\frac{\partial^2z}{\partial x\partial y^{ }}$

6.

If the number of arbitrary constants is less than or equal to number of independent variables then the pde obtained is of order

a)

>1

b)

=1

c)

<1

7.

If the number of arbitrary function is n then the pde obtained is of order

a)

<n

b)

>n

c)

=n

d)

1

8.

The complete integral is defined as

a)

The number of arbitrary constants < The number of independent variables

b)

The number of arbitrary constants = The number of independent variables

c)

The number of arbitrary constants > The number of independent variables

9.

Giving particular values for arbitrary constants in the complete integral is called

a)

Particular solution

b)

General solution

c)

Singular solution

10.

which of the following has the trial solution z=ax+by+c

a)

$z=px+qy+p^2$

b)

$p+q=pq$

c)

$p\left(1+q\right)=qz$

11.

Which of the following is clairaut's form

a)

$z=px+qy+\sqrt{pq}$

b)

$p+q=1$

c)

$p+q=x+y$

12.

The complete integral of $F_1\left(x,p\right)=F_2\left(y,q\right)$ is

a)

$z=\int_{ }^{ }qdx+\int_{ }^{ }pdy$

b)

$z=\int_{ }^{ }pdx-\int_{ }^{ }qdy$

c)

$z=\int_{ }^{ }pdx+\int_{ }^{ }qdy$

13.

The subsidiary equation for Lagrange's linear equation

a)

$\frac{dx}{x}=\frac{dy}{y}=\frac{dz}{z}$

b)

$\frac{dx}{p}=\frac{dy}{q}=\frac{dz}{r}$ $\frac{dx}{p}=\frac{dy}{q}=\frac{dz}{r}$

c)

$\frac{dx}{P}=\frac{dy}{Q}=\frac{dz}{R}$

14.

The multipliers for $x\left(y-z\right)p+y\left(z-x\right)q=z\left(x-y\right)$ is

a)

$1,1,1\ and\ \frac{1}{x},\frac{1}{y},\frac{1}{z}$

b)

$1,1,1\ and\ x,y,z$

c)

$0,0,0\ and\ 1,1,1$

15.

$The\ CF\ of\ \left(D^2-DD'-2D'^2\right)z=0$

a)

$f_1\left(y-2x\right)+f_2\left(y-x\right)$

b)

$f_1\left(y+2x\right)+f_2\left(y+x\right)$

c)

$f_1\left(y+2x\right)+f_2\left(y-x\right)$

Partial Differential Equations

Total questions: 15

Worksheet time: 10mins

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