Free Printable PDE

1.

Which of the following is an example for first order linear partial differential equation?

a)

Lagrange’s Partial Differential Equation

b)

Clairaut’s Partial Differential Equation

2.

What is the nature of Lagrange’s linear partial differential equation?

a)

First-order, Second-degree

b)

Second-order, First-degree

c)

First-order, Third-degree

d)

First-order, First-degree

3.

Find the general solution of the linear partial differential equation, yzp+zxq=xy.

a)

$\phi\left(x^2-y^2,y^2-z^2\right)=0$

b)

$\phi\left(x^2-z^2,\ y^2-z^2\right)=0$

c)

$\phi\left(x^2-y^2,-z^2\right)=0$

d)

$\phi\left(x^2-y^2,y^2-x^2\right)=0$

4.

Which of the following equations represents Clairaut’s partial differential equation?

a)

z=px+f(p,q)

b)

z=f(p,q)

c)

z=p+q+f(p,q)

d)

z=px+qy+f(p,q)

5.

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

a)

$f\left(\frac{x}{y},\frac{y}{z}\right)=0$

b)

$f\left(\frac{x}{y},\frac{x}{z}\right)=0$

c)

$f\left(\frac{y}{x},\frac{y}{z}\right)=0$

d)

$f\left(\frac{y}{x},\frac{x}{z}\right)=0$

6.

The solution of non-linear partial differential equation

\sqrt{p}+\sqrt{q}=1

is

a)

$z=ax+\left(1-\sqrt{a}\right)^2\ y+c$

b)

$z=ax+ay+b$

c)

$z=ax+2ay+c$

d)

$z=\sqrt{a}x+ay+c$

7.

The solution of non-linear partial differential equation

\sqrt{p}+\sqrt{q}=x

is

a)

$z=\left(x-a\right)^3+a^2y+b$

b)

$z=\frac{\left(x-a\right)^3}{3}+a^2y+b$

c)

$z=\left(x-a\right)^3+b$

d)

$z=a^2x+\left(y-a\right)^3+c$

8.

The solution of non-linear partial differential equation

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

is

a)

$\log\left(az-1\right)=x+a\ y+c$

b)

$\log z=x+a\ y+c$

c)

$az-1=e^{x+a\ y+c}$

9.

The solution of non-linear partial differential equation

q-p+x-y=0

is

a)

$z=\frac{\left(x+a\right)^2}{2}+\frac{\left(y+a\right)^2}{2}+c$

b)

$z=\left(x+a\right)^2+\left(y+a\right)^2+c$

c)

$z=\frac{\left(x+a\right)^2}{2}+\frac{\left(y-a\right)^2}{2}+c$

d)

$z=\frac{\left(x-a\right)^2}{2}+\frac{\left(y+a\right)^2}{2}+c$

PDE

Total questions: 9

Worksheet time: 45mins

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