Help me solving this differential equation

In summary, a differential equation is a mathematical equation used to describe the relationship between a function and its derivatives. There are various methods for solving differential equations, including separation of variables, integrating factors, and using power series or Laplace transforms. A basic understanding of calculus is necessary for solving differential equations. Real-life applications of differential equations include modeling population growth and pendulum motion. Software programs such as Mathematica, MATLAB, and Maple can assist with solving differential equations using numerical methods.
  • #1
6
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[/yy] + [/zz] - ∂p/∂x = 0;

∂u/∂x = 0;

∂p/∂x = constant


i tried separation of variables ...
 
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  • #3
μ[uyy + uzz] - ∂p/∂x = 0 ... (1)

∂u/∂x = 0 ;

now i assumed u(y,z) = Y(y)Z(z)

so (1) becomes ... μ[ZYyy + YZzz] - ∂p/∂x = 0

hence (1/Y)*Yyy + (1/Z)*Zzz = (R/YZ) = -λ2
where, R = (1/μ)*∂p/∂x

now Yyy + λ2Y = 0 ... can be solved easily but what about the remaining part ... i couldn't solve it due to the constant
 

1. Can you explain what a differential equation is?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model many natural phenomena in fields such as physics, engineering, and economics.

2. How do you approach solving a differential equation?

There are various methods for solving differential equations, depending on the type and complexity of the equation. Some common approaches include separation of variables, integrating factors, and using power series or Laplace transforms.

3. Is it necessary to know calculus to solve differential equations?

Yes, a basic understanding of calculus is necessary to solve differential equations. This includes knowledge of derivatives, integrals, and basic concepts such as the chain rule and product rule.

4. Can you provide an example of a real-life application of differential equations?

Differential equations are used to model many real-life situations, such as the growth of a population, the spread of diseases, and the motion of objects under the influence of forces. For example, the motion of a pendulum can be described using a differential equation.

5. Are there any software programs that can help with solving differential equations?

Yes, there are many software programs, such as Mathematica, MATLAB, and Maple, that can help with solving differential equations. These programs use numerical methods to approximate solutions and can handle complex and non-linear equations.

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