How to Solve a Non-Separable Differential Equation?

In summary, the given equation is dy/dx = -(4x+4y) / (4x+4y-2) and the given value is v = x + y. The mistake in the attempted solution was that dv/dx should be 1 + dy/dx instead of x + dy/dx. The correct solution is - (x+y)^2 + (x+y) = x + A.
  • #1
hotjohn
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1

Homework Statement


i was given dy/dx = -(4x+4y) / (4x+4y-2) , v= x +y . I have tried to do ( as in the photo) , but I didn't get the ans , in the last line of my working , the V and x are not separable , which part of my working is wrong ?

Homework Equations

The Attempt at a Solution

 

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  • #2
If v = x+y, then dv/dx = 1 + dy/dx, not x + dy/dx as you wrote.
 
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  • #3
phyzguy said:
If v = x+y, then dv/dx = 1 + dy/dx, not x + dy/dx as you wrote.
i have redone the question , but i gt stucked here , how to proceed?

btw , the ans given is - ( (x+y) ^2 ) +(x+y ) = x +A
 

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  • #4
Check your signs again.
 
  • #5
phyzguy said:
Check your signs again.
ok , i gt it correct now , thanks
 

Related to How to Solve a Non-Separable Differential Equation?

1. What is a form differential equation?

A form differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is a way of expressing a relationship between a function and its rate of change over time or space.

2. Why are form differential equations important in science?

Form differential equations are important in science because they allow us to model and understand complex physical phenomena. They are used in many fields such as physics, engineering, chemistry, and biology to describe the behavior of systems and predict future outcomes.

3. How do you solve a form differential equation?

Solving a form differential equation involves finding a function that satisfies the equation. This can be done using various mathematical techniques, such as separation of variables, substitution, or using special functions. In some cases, numerical methods may also be used to approximate a solution.

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

The main difference between an ordinary differential equation (ODE) and a partial differential equation (PDE) is that an ODE involves only one independent variable, while a PDE involves multiple independent variables. ODEs are commonly used to model systems that change over time, while PDEs are used to model systems that change over both time and space.

5. How are form differential equations used in real-world applications?

Form differential equations have a wide range of applications in various fields, including physics, engineering, economics, and biology. They are used to model and analyze systems such as population growth, chemical reactions, fluid flow, and electrical circuits. They also play a crucial role in the development of technologies such as computer simulation and control systems.

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