Help solving a Differential equation

In summary, a differential equation is a mathematical equation that describes the relationship between a function and its derivatives. They are important in science for modeling and understanding complex systems and can be solved using methods such as separation of variables and Laplace transforms. There are two types of differential equations - ordinary (ODE) and partial (PDE) - with different numbers of independent variables and derivatives. These equations can be solved both analytically and numerically, depending on the complexity and desired level of accuracy.
  • #1
real10
39
0
k is an integer greater than 1.
[tex]y'=y^{\frac{-1}{k}}[/tex]
solving this ode in MATLAB gives me this
[tex](\frac{t*k+t+C1*k}{k})^{\frac{k}{1+k}}[/tex] which is correct since the further part of the problem proving a certain limit involving y follows from using the above MATLAB sol.

I am interested in solving this ode by hand.

by hand I am getting [tex]y^{\frac{k+1}{k}}=kt[/tex]
 
Last edited:
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  • #2
never mind I have solved it:smile:
 
  • #3
I have a problem in heat equation. Can ADI Methods be used in Cylindrical coordinate system?
Any help should be appreciated.
 

What is a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves one or more variables and their rates of change over time or space.

Why are differential equations important in science?

Differential equations are important in science because they help us model and understand complex systems in various fields such as physics, engineering, economics, and biology. They are also used to predict future behavior and make informed decisions.

What methods are used to solve differential equations?

There are several methods used to solve differential equations, including separation of variables, substitution, and the use of integrating factors. Other methods include Laplace transforms, power series, and numerical methods.

What is the difference between a ordinary and a partial differential equation?

An ordinary differential equation (ODE) involves a single independent variable, while a partial differential equation (PDE) involves multiple independent variables. ODEs also have one or more ordinary derivatives, while PDEs have partial derivatives.

Can differential equations be solved analytically or numerically?

Yes, differential equations can be solved both analytically and numerically. Analytical solutions involve finding an explicit formula for the solution, while numerical solutions use algorithms to approximate the solution. The choice of method depends on the complexity of the equation and the desired level of accuracy.

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