Free Printable Partial Differential Equations

1.

A partial differential equation requires

a)

exactly one independent variable

b)

two or more independent variables

c)

more than one dependent variable

d)

equal number of dependent and independent variables

2.

Using substitution, which of the following equations are solutions to the partial differential equation?

a)

b)

c)

d)

3.

The partial differential equation

is classified as

a)

elliptic

b)

parabolic

c)

hyperbolic

d)

none of the above

4.

The partial differential equation

is classified as

a)

elliptic

b)

parabolic

c)

hyperbolic

d)

none of the above

5.

The complete integral of $z=px+qy+f\left(p,q\right)$

a)

$z=px+qy$

b)

$z=ax+by+f\left(a,b\right)$

c)

$z=f\left(a,b\right)$

d)

none of the above

6.

What is the order & degree of the p.d.e $x^2\left(\frac{\partial z}{\partial x}\right)^2=z\left(x-y\frac{\partial z}{\partial y}\right)$

a)

1 & 2

b)

2 & 1

c)

2 & 2

d)

none of the above

7.

Singular solution of Partial differential equation can be obtained by

a)

General solution

b)

Complete solution

c)

both a & b

d)

none of the above

8.

The condition of compatibility of partial differential equations $f\left(x,y,z,p,q\right)=0\ ,\ \ g\left(x,y,z,p,q\right)=0$ is

a)

$\frac{\partial\left(f,g\right)}{\partial\left(p,q\right)}=0$

b)

$\frac{\partial\left(f,g\right)}{\partial\left(p,q\right)}\ne0$

c)

$\frac{\partial\left(f,p\right)}{\partial\left(g,q\right)}=0$

d)

$\frac{\partial\left(f,q\right)}{\partial\left(g,p\right)}\ne0$

9.

If u is homogeneous function of order n then $\frac{\partial u}{\partial x}\ ,\ \frac{\partial u}{\partial y}$ both are homogeneous function of order

a)

n

b)

n-1

c)

n+1

d)

n-2

10.

If $f\left(x,y\right)=0\$ then what is the value of $\frac{dy}{dx}$ is

a)

$\frac{f_x}{f_y}$

b)

$-\frac{f_x}{f_y}$

c)

$\frac{f_y}{f_x}$

d)

$-\frac{f_y}{f_x}$

Partial Differential Equations

Total questions: 10

Worksheet time: 5mins

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