Purchase Solution

Solving Partial Differential Equations by Change of Variables and Characteristic Curves

Not what you're looking for?

Ask Custom Question

In solving this problem, derive the general solution of the given equation by using an appropriate change of variables.

1. ∂u/∂t - 2 ∂u/∂x = 2

Answer: u(x,t) = f(x + 2t) - x

In this exercise, (a) solve the given equation by the method of characteristic curves, and (b) check you answer by plugging it back into the equation.

2. ∂u/∂x + x2 ∂u/∂y = 0

Answer: (a) u(x,y) = f(1/3 x3 - y)

Attachments
Purchase this Solution
Solution Summary

Solving Partial Differential Equations by Change of Variables and Characteristic Curves is investigated. The solution is detailed and well presented.

Purchase this Solution
Free BrainMass Quizzes
Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

View More Free Quizzes
Related BrainMass Solutions

  • Characteristic curves

    446928 Characteristic curves Find a partial differential equation whose characteristic curves are the lines x-y=a, x+2y=b where a,b are arbitrary real constants. see attachment Problem: Find a partial differential equation whose characteristic curves

  • Partial Differential Equations : Characteristic Curves

    117454 Partial Differential Equations : Characteristic Curves 1.(a) Solve the given equation by the method of characteristic curves. (b) Check your answer by plugging it back into the equation.

  • Cross-eyed heart

    28848 Differential Equations - Cross-Eyed Heart 27. y'' + 25y = sin(4t), y(0) = 0, y'(0) = 0. Plot the component curves and the orbit, the latter for the rectangle |y|< 0.25 and |y'|< 1. Any surprises? 28.

  • PDE with Time-Dependent Domain

    This problem is taken from Partial Differential Equations: Analytical Solution Techniques, by J. Kevorkian.

  • solving differential equations

    Solve the differential equation, y is a function of x So this DE can be solved by separation of variables.

  • Solving Differential Equations with given initial conditions

    different methods to solving different kind of differential equations.

  • Normal Modes : Second Order Simultaneous Equations

    The question asks for x(t) and y(t), which is implied that we have to deal with the problems of solving differential equations and solving simultaneous equations.

  • Transforming Partial Differential Equations

    This solution explains the transformation of the partial differential equation into a new partial differential equation by changing the variables. The solution is given in detail.

  • Partial differential equations

    38632 Partial Differential Equations A) Classify and find general expressions for the characteristic coordinates for the equation {see attachment} b) Use the canonical coordinates {see attachment} and transfer the above PDE into the new coordinates

View More Related Solutions