How Do You Solve the Differential Equation 6yy' = x?

Thread starter mr_coffee
Start date Jan 18, 2006
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In summary, differential equations involve derivatives and are used to describe rate of change, while integral equations involve integration and are used to find total value. Differential equations are useful for modeling systems involving change over time, and can be solved using methods such as separation of variables and substitution. The choice between numerical and analytical methods for solving differential equations depends on the complexity and desired accuracy. Differential equations have real-world applications in fields such as economics, biology, and engineering.

Jan 18, 2006

mr_coffee

hello everyone, this is probably simple but its in a weird form or maybe I'm just not seeing it:
6yy' = x; y(6) = 4;

Is x = g(x) and 6 = p(x)?
or is this not an integrating factor?

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Jan 18, 2006

benorin

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It's separable: 6ydy = xdx

Jan 18, 2006

mr_coffee

wow that was easy, thank you for the fast repsonce!, i don't know why i had a brain fart there:
sqrt(x^2/6+10)

FAQ: How Do You Solve the Differential Equation 6yy' = x?

What is the difference between differential and integral equations?

Differential equations involve the derivatives of a function, while integral equations involve the integration of a function. Differential equations are used to describe rate of change, while integral equations are used to find the total value of a function over a certain interval.

When should I use differential equations?

Differential equations are useful for modeling systems that involve change over time, such as motion, population growth, and chemical reactions. They are also used in engineering and physics to describe the behavior of systems.

What are the different methods for solving differential equations?

There are several methods for solving differential equations, including separation of variables, substitution, and using power series. The appropriate method to use depends on the type of differential equation and initial conditions given.

Which is better: numerical or analytical methods for solving differential equations?

Numerical methods involve using algorithms and computers to approximate solutions to differential equations, while analytical methods involve finding exact solutions using mathematical formulas. The choice of method depends on the complexity of the equation and the desired level of accuracy.

Are there real-world applications for differential equations?

Yes, differential equations are used in various fields such as economics, biology, and ecology to model and understand real-world phenomena. They are also used in engineering to design and analyze systems and processes.