• anonymous
can anyone explain me the form of first and higher order linear differential equation? I know the form of linear differential equation. e.g. y''-xy'+2y=0. So what will happen to this equation if the coefficient of y' is y?
Differential Equations
  • Stacey Warren - Expert
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
  • schrodinger
I got my questions answered at in under 10 minutes. Go to now for free help!
  • UnkleRhaukus
A simple example where the coefficient of the highest order term (y') : is y \[y\cdot y'=a\] Because the co-efficient is not a constant, this equation is non-linear.
  • anonymous
While you are correct with your example being non-linear, in general the non-constancy of coefficients is insufficient to classify an ODE as non-linear. As the poster noted, their ODE was a linear ODE even though the coefficient on the y' term is a function of x namely f(x)=-x. A better way of stating it is that as long as the "coefficient" (aka the function) multiplying each term is not a function of the independent variable (y) or its derivatives, then the ODE is linear. Otherwise the ODE is non-linear. The example you provided is precisely such a term that would make an ODE non-linear. Other examples of non-linear terms y^2 or (y')^2.

Looking for something else?

Not the answer you are looking for? Search for more explanations.