Solving the IVP: du/dx*du/dy = xy with IC u(x,y) = x for y = 0

Thread starter jessey_7
Start date Jul 13, 2007
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Ivp

In summary, the initial conditions for an IVP are typically given in the problem statement and consist of a known function value at a specific initial point. The first step in solving an IVP is to rewrite it as a system of first-order differential equations. The choice of method for solving an IVP depends on the specific problem and its characteristics, and the initial point must fall within the domain of the problem. To check the accuracy of a solution to an IVP, the initial conditions can be plugged in and evaluated at the initial point to ensure that they satisfy the differential equation and initial conditions.

Jul 13, 2007

jessey_7

pde : du/dx*du/dy = xy

IC: u(x,y) = x for y = 0

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Jul 13, 2007

Dick

Science Advisor

Homework Helper

Separation of variables is always a good thing to try first. And it works in this case.

FAQ: Solving the IVP: du/dx*du/dy = xy with IC u(x,y) = x for y = 0

How do I determine the initial conditions for an IVP?

The initial conditions for an IVP (initial value problem) are typically given in the problem statement. They consist of a known function value at a specific initial point, which is often denoted as x₀ and y₀.

What is the first step in solving an IVP?

The first step in solving an IVP is to rewrite it as a system of first-order differential equations. This involves breaking down the higher-order equation into a set of equations that each describe the rate of change of a single variable.

How do I choose a suitable method for solving an IVP?

The choice of method for solving an IVP depends on the specific problem and its characteristics. Some commonly used methods include Euler's method, Runge-Kutta methods, and numerical methods such as the finite difference method or finite element method.

Can I use any initial point to solve an IVP?

No, the initial point must be within the domain of the problem. This means that the initial point must fall within the range of x-values for which the differential equation is defined.

How do I know if my solution to an IVP is correct?

You can check the accuracy of your solution by plugging in the initial conditions and evaluating the differential equation at the initial point. The solution should satisfy the differential equation and initial conditions.