Free Printable PDE: formation and lagranges

1.

An equation containing partial derivatives of one or more dependent variables of two or more independent variables

a)

Ordinary Partial Differential Equation

b)

Partial Differential Equation

c)

Ordinary Differential Equation

d)

Partially Ordinary Differential Equation

2.

Find the differential equation of all spheres of fixed radius having centre in xy -plane. hint:

\left(x-a\right)^2+\left(y-b\right)^2+z^2=r^2

a)

$z^2\left(p^2+q^2+1\right)=r^2$

b)

$z^2\left(p^2+q^2\right)=r^2$

c)

$p^2+q^2+1=r^2$

3.

What is the PDE when the arbitrary constants a and b are eliminated from

z=\left(x-a\right)^2+\left(y-b\right)^2

a)

$p^2+q^2=4z$

b)

$p^2-q^2-4z=0$

c)

$p^2q^2=4z$

d)

None

4.

What is the PDE when the arbitrary constants a and b are eliminated from

ax^2+by^2=1-z^2

a)

$zxp+zyq=z^2-1$

b)

$zxp+zyq=z^2+1$

c)

None

5.

What is the PDE when the arbitrary constants a and b are eliminated from

z=axy+b

a)

$xp+yq=1$

b)

$xp-yq=0$

c)

None

6.

Obtain partial differential equation by eliminating the arbitrary function from the given equation.

z=f\left(x^2+y\right)+g\left(x^2-y\right)

a)

$rx-p=4x^3t$

b)

$rx-t=4x^3p$

c)

$rx-q=4t$

d)

none

7.

obtain PDE by eliminating arbitrary functions from the given equation

z=\phi\left(x^2-y^2\right)

a)

px+qy=0

b)

py+qx=0

c)

p/x+q/y=9

d)

x/p+y/q=0

8.

The solution of Lagrange's partial differential equation xp+yq=z

a)

$f\left(\frac{x}{y},\frac{y}{z}\right)$

b)

$f\left(\frac{x}{y},\frac{x}{z}\right)$

c)

$f\left(\frac{x}{z},\frac{y}{z}\right)$

d)

$f\left(\frac{y}{x},\frac{y}{z}\right)$

9.

The solution of Lagrange's partial differential equation xp+zq=y

a)

$f\left(y^2-z^2,\frac{y}{x+z}\right)$

b)

$f\left(y^2-z^2,\frac{x}{y+z}\right)$

10.

The solution of Lagrange's partial differential equation $\left(1-x\right)p+\left(2-y\right)q=3-z$

a)

$f\left(\frac{2-y}{1-x},\frac{3-z}{2-y}\right)$

b)

$f\left(\frac{3-y}{2-x},\frac{1-z}{2-y}\right)$

c)

$f\left(\frac{2-x}{1-z},\frac{3-x}{2-y}\right)$

PDE: formation and lagranges

Total questions: 10

Worksheet time: 50mins

Similar Resources on Wayground