MeMoses said:Homework Statement
[itex]\frac{dy}{dx}=\frac{2y - x + 7}{4x - 3y -18}[/itex]
Homework Equations
The Attempt at a Solution
I tried using v = y/x and got nothing. Same goes for trying to find an integrating factor to make the equation exact. I am given a hint, Find h and k so that the substitution x = u+h, y=v+k transforms the above to a homogenous differential equation. I'm not sure what the means or how I'm supposed to use that. Thanks for any help.
A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves the use of derivatives to express a relationship between a dependent variable and one or more independent variables.
A linear differential equation is one in which the unknown function and its derivatives appear only in a linear combination. In contrast, a nonlinear differential equation is one in which the unknown function and its derivatives appear in a nonlinear combination.
A nonexact differential equation is a type of nonlinear differential equation where the integrating factor is not a function of the independent variable. This means that the equation cannot be solved by using the traditional method of separation of variables.
A differential equation is considered nonlinear if it contains terms that involve the unknown function or its derivatives in a nonlinear way. For example, if the equation contains terms like sin(x) or x^2, it is a nonlinear equation.
Some common techniques for solving nonlinear differential equations include using power series, substitution, and numerical methods such as Euler's method or the Runge-Kutta method. Another approach is to transform the equation into a linear differential equation through a change of variables.