Partial differential - difference of opinion

In summary, partial differential equations involve derivatives with respect to multiple independent variables, while difference equations involve differences between values at different points or times. They are used to model physical phenomena in fields such as physics, engineering, and biology, and can also be used to solve optimization problems and make predictions. Boundary conditions are important in determining a unique solution to the equation and can significantly impact the behavior of the system being modeled. Numerical methods, such as finite difference or finite element methods, can be used to approximate the solution to a partial differential equation by discretizing the domain and solving the resulting system of equations. While some simple partial differential equations can be solved analytically, most real-world problems require numerical methods to find a solution.
  • #1
Roodles01
128
0
I have a difference of opinion with 2 calculation engines.

equation to solve is;
d/dx (a(x^2 +y)

Wolframalpha of course is a very trusted source but I also use symbolab.
Here is a screenshot of the differential I want from both sites and associated answers.
partial diff symbolab.JPG


. . . and the wolfram solution

partial diff wolfram.JPG


could anyone please confirm which is correct.
Personally I like the symbolab solution.
 
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  • #2
The point is, wolfram assumed you mean a is a function and its argument is [itex] x^2+y [/itex]. You should have written a*(x^2+y).
 
  • #3
oops sorry. Just me being lazy
 

1. What is the difference between a partial differential equation and a difference equation?

Partial differential equations involve derivatives with respect to multiple independent variables, while difference equations involve differences between values at different points or times.

2. How are partial differential equations used in science?

Partial differential equations are used to model physical phenomena in fields such as physics, engineering, and biology. They can also be used to solve optimization problems and make predictions.

3. What is the importance of boundary conditions in solving partial differential equations?

Boundary conditions specify the behavior of a partial differential equation at the edges of the domain. They are crucial in determining a unique solution to the equation and can significantly impact the behavior of the system being modeled.

4. How do you numerically solve a partial differential equation?

Numerical methods, such as finite difference or finite element methods, can be used to approximate the solution to a partial differential equation. These methods involve discretizing the domain and solving the resulting system of equations.

5. Can partial differential equations be solved analytically?

Some simple partial differential equations can be solved analytically using techniques such as separation of variables or the method of characteristics. However, most real-world problems require numerical methods to find a solution.

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