Partial Differential Equations

A partial differential equation requires

• exactly one independent variable

• two or more independent variables

• more than one dependent variable

• equal number of dependent and independent variables

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

                     

• 
• 
• 
• 

The partial differential equation

is classified as

• elliptic

• parabolic

• hyperbolic

• none of the above

The partial differential equation

is classified as

• elliptic

• parabolic

• hyperbolic

• none of the above

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

•  $z=px+qy$  

•  $z=ax+by+f\left(a,b\right)$  

•  $z=f\left(a,b\right)$  

• none of the above

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

• 1 & 2

• 2 & 1

• 2 & 2

• none of the above

Singular solution of Partial differential equation can be obtained by

• General solution

• Complete solution

• both a & b

• none of the above

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

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

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

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

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

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 

• n

• n-1

• n+1

• n-2

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

•  $\frac{f_x}{f_y}$  

•  $-\frac{f_x}{f_y}$  

•  $\frac{f_y}{f_x}$  

•  $-\frac{f_y}{f_x}$