Solution of two first order differential equation with one algebraic equation.

In summary, the conversation is about solving two first order differential equations with one algebraic equation. The person is able to get a solution for the problem by solving the differential equations, but is unsure of how to incorporate the algebraic equation into the solution. It is suggested to check if the initial conditions are consistent with the algebraic relationship, as there may be a mistake in the wording of the problem. The person confirms that the algebraic equation is not satisfying the initial condition.
  • #1
rickyvery
2
0
Dear Friends

i am trying to solve two first order differential eqs. with one algebraic eq.

i am able to get solution of problem by simply solving two first order differential eqs. i do not know how to incorporate algebraic eq with my solution.

please see attachment

thanks in advance

Ricky
 

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  • #2
Hi !
did you check if the initial conditions are consistent with the algebric relationship ?
If not, there is a mistake in the wording of the problem.
 
  • #3
JJacquelin said:
Hi !
did you check if the initial conditions are consistent with the algebric relationship ?
If not, there is a mistake in the wording of the problem.

Dear JJacquelin,

You are right. algebraic equation is not satisfying initial condition.

thanks for your reply.

Ricky
 

What is a first order differential equation?

A first order differential equation is an equation that relates a function to its derivative. It involves only the first derivative of the function and can be written in the form dy/dx = f(x,y).

What is an algebraic equation?

An algebraic equation is an equation that contains one or more variables and can be solved using algebraic operations such as addition, subtraction, multiplication, and division.

What is the solution of a differential equation?

The solution of a differential equation is the function that satisfies the equation. It is obtained by integrating the differential equation and adding a constant of integration.

How can two first order differential equations be solved with one algebraic equation?

This can be done by solving one of the differential equations for one of the variables and substituting it into the other differential equation. This results in an algebraic equation that can be solved to find the value of the remaining variable, which can then be used to solve for the first variable.

What are some applications of solving two first order differential equations with one algebraic equation?

This technique is commonly used in physics and engineering to model and solve problems involving systems with changing variables. It can also be used in population dynamics, chemical reactions, and financial modeling, among others.

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