Free Printable First Order PDEs

1.

Find the complete integral of pq=1 .

a)

i) z=(1/b)x+by+c

b)

ii) z=ax+(1/a)y+c

c)

iii) z=ax+by+c

d)

(i)&(ii)

2.

Find the singular integral of z=px+qy+pq

a)

z=x+y+1

b)

z+xy=0

c)

xy-z=0

d)

zx+y=0

3.

By usual notations what is the general form of Lagrange’s linear PDE.

a)

pdx+qdy=0

b)

Pp+Qq=R

c)

Pdx+Qdy=Rdz

d)

non of the above

4.

Solve: p+q=1

a)

i) f(x-y,y-z)=0

b)

ii) f(x-y, x-z)=0

c)

both (i)&(ii)

d)

none

5.

Solve: px+qy=z

a)

i) φ(x/y, y/z,)

b)

ii) φ(x/y, x/z,)

c)

both (i)&(ii)

d)

none

6.

What are the Lagrange’s multipliers while solving the PDE

px-qy=y^2-x^2

a)

$x,y,z$

b)

$1,1,1$

c)

$y,x,1$

d)

$x,y,1$

7.

What are the Lagrange’s multipliers while solving the PDE

px\left(y-z\right)+qy\left(z-x\right)=z\left(x-y\right)

a)

$x,y,z$

b)

$1,1,1$

c)

$y,x,1$

d)

$x,y,1$

8.

What are the Lagrange’s multipliers while solving the PDE

p\left(y-z\right)-q\left(2x+y\right)=2x+z

a)

$x,y,z$

b)

$2x,y,z$

c)

$x,-2y,z$

d)

$2x,-z,-y$

9.

What are the multiples while solving $\left(3z-4y\right)p+\left(4x-2z\right)q=2y-3x$

a)

$2,3,4$

b)

$3,4,2$

c)

$4,2,3$

d)

$1,1,1$

10.

For which type of the PDE the singular integral does exist

a)

$F\left(p,q\right)=0$

b)

$z=px+qy+f\left(p,q\right)$

c)

$F\left(z,p,q\right)=0$

d)

none

First Order PDEs

Total questions: 10

Worksheet time: 6mins

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