Partial Differential Equations

If we eliminate a and b from z = (x+a)(y+b)

• z = p/q

• z = p - q

• z = p + q

• z = pq

If the number of constants to be eliminated is equal to number of independent variables, then the result is_____

• First order PDE

• Second order PDE

• third order PDE

• Second order linear PDE

If the number of constants to be eliminated is greater than the number of independent variables, then the result is_____

• First order PDE

• Second and higher order PDE

• Second and higher order PDE

• only Second order linear PDE

The Clairaut’s equation is of the form____

• y=px+f(p)

• y=px+f(q)

• x=qy+f(p)

• x=py+f(q)

If the equation is in the form f(x, p, q)=0, then we assume

• p=a

• z=pq

• q=a

• p=aq

The solution of the equation z = px + qy + pq is____

• z = ax + by + pq

• z = ax + by + ab

• z = bx + ay + ab

• z = px + qy + ab

Eliminate the arbitrary function from z = f(x²+y²)

• px = qy

• py+qx=0

• px+qy=0

• py = qx

Eliminate the arbitrary constants c and r from x²+y²+(z-c)²=r²

• px = qy

• px+qy=0

• py = qx

• py+qx=0

A solution containing as many arbitrary constants as there are independent variables is called____

• complete integral

• particular integral

• singular integral

• general integral

A solution obtained by giving particular values to the arbitrary constants in a complete integral is called____

• complete integral

• particular integral

• singular integral

• general integral