PDE First and Higher Order Quiz

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

• Lagrange’s Partial Differential Equation

• Clairaut’s Partial Differential Equation

Answer explanation

Lagrange’s Partial Differential Equation is an example of a first-order linear partial differential equation.

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

• First-order, Second-degree

• Second-order, First-degree

• First-order, Third-degree

• First-order, First-degree

Answer explanation

Lagrange's linear partial differential equation is First-order, First-degree.

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

Answer explanation

The correct choice is phi(x^2-y^2, y^2-z^2)=0 because it represents the general solution of the given linear partial differential equation.

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

• z=px+f(p,q)

• z=f(p,q)

• z=p+q+f(p,q)

• z=px+qy+f(p,q)

Answer explanation

The correct choice is z=px+qy+f(p,q) because it represents Clairaut’s partial differential equation.

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

Answer explanation

The correct solution of Lagrange's partial differential equation xp+yq=z is f(x/y, y/z)=0.

Answer explanation

The correct choice is z=ax+(1-√a)^2y+c because it satisfies the given non-linear partial differential equation.

Answer explanation

The correct choice is z=(x-a)^3/3+a^2y+b because it satisfies the given non-linear partial differential equation.

Answer explanation

The correct choice is \(\log\left(az-1\right)=x+a\ y+c\) because it represents the solution of the given non-linear partial differential equation.

Answer explanation

The correct choice is z=(x+a)^2/2+(y+a)^2/2+c, which satisfies the given non-linear partial differential equation.

An equation containing partial derivatives of one or more dependent variables of two or more independent variables

• Ordinary Partial Differential Equation

• Partial Differential Equation

• Ordinary Differential Equation

• Partially Ordinary Differential Equation

Answer explanation

A Partial Differential Equation involves partial derivatives of dependent variables with respect to multiple independent variables.