Partial Differential Equations

A PDE consists of

• only one independent variable

• more than one independent variable

• more than one dependent varible

The highest derivative in the given pde is called

• order

• degree

The degree of the following pde  $\left(\text{}\frac{\partial z}{\partial x}\ \right)^2+2\left(\frac{\partial^2z}{\partial x\partial y}\right)+\left(\frac{\partial z}{\partial y}\right)^2=0$  is

• 2

• 0

• 1

The order of the following pde  $\left(z_{xx}\right)^2+\left(z_{xyy}\right)+\left(z_{yy}\right)=\sin z$  is

• 1

• 2

• 3

The expansion for s

• $\frac{\partial^2z}{\partial y^2}$

• $\frac{\partial^2z}{\partial x^2}$

• $\frac{\partial^2z}{\partial x\partial y^{ }}$

If the number of arbitrary constants is less than or equal to number of independent variables then the pde obtained is of order

• >1

• =1

• <1

If the number of arbitrary function is n then the pde obtained is of order

• <n

• >n

• =n

• 1

The complete integral is defined as

• The number of arbitrary constants < The number of independent variables

• The number of arbitrary constants = The number of independent variables

• The number of arbitrary constants > The number of independent variables

Giving particular values for arbitrary constants in the complete integral is called

• Particular solution

• General solution

• Singular solution

which of the following has the trial solution z=ax+by+c

• $z=px+qy+p^2$

• $p+q=pq$

• $p\left(1+q\right)=qz$