Solving a Third Order Differential Equation with Initial Conditions

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In summary, a third order differential equation is an equation in which the highest derivative present is of third order. The general form of a third order differential equation is y''' = f(x, y, y', y'') where f(x, y, y', y'') is a function of the independent variable x and the dependent variable y and its first, second, and third derivatives. The significance of the third order DE (y'''=3*y*y') lies in its use for modeling systems where the rate of change is proportional to the square of the variable and its third derivative. To solve a third order differential equation, one must find a particular solution that satisfies the given equation and its initial conditions, which can be done analyt
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math_addict
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I'm interested in solving this 3rd order DE y'''=3*y*y' with conds y(0)=-2, y'(0)=0, y''(0)=4,5. Thanks for any ideas.. I've the right solution, but the problem is how to achieve it.
 
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[tex]\frac{3}{2}\frac{d}{dt}(y^2)=3y\dot{y}[/tex]
 

1. What is a third order differential equation?

A third order differential equation is an equation in which the highest derivative present is of third order. It involves finding a function that satisfies the given equation and its first, second and third derivatives.

2. What is the general form of a third order differential equation?

The general form of a third order differential equation is y''' = f(x, y, y', y'') where f(x, y, y', y'') is a function of the independent variable x and the dependent variable y and its first, second, and third derivatives.

3. What is the significance of the third order DE (y'''=3*y*y')?

The third order DE (y'''=3*y*y') is a type of non-linear differential equation. It is used to model systems where the rate of change of a variable is proportional to the square of the variable itself, and the third derivative of the variable. It has applications in physics, chemistry, and engineering.

4. How do you solve a third order differential equation?

Solving a third order differential equation involves finding a particular solution that satisfies the given equation and its initial conditions. This can be done analytically using techniques such as separation of variables, or numerically using methods such as Euler's method or Runge-Kutta methods.

5. What are the initial conditions for a third order differential equation?

The initial conditions for a third order differential equation are the values of the dependent variable and its first, second, and third derivatives at a specific initial point. These initial conditions are necessary to determine the particular solution of the differential equation.

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