Is there such a thing as a "rocket license" in the US? Isn't this equation linear differential equation? What do professors do if they receive a complaint about incompetence of a TA? Solving differential equation with the Dirac Delta Function, Solving differential equation with impulse function. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. How to get my parents to take my Mother's cancer diagnosis seriously? How can i show that this differential equation is exact? $$ I came across this in a research paper and the answer is given but the method to solve it isn't. But when we substitute this expression into the differential equation to find a value for \(A\),we run into a problem. What are the effects of sugar in cat food? Why would a circuit designer use parallel resistors? How to tell whether a differential equation is linear or non-linear when it can be expressed in both forms? I'm unable to understand why the differential equation mentioned above is not linear. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Let me edit the question and add in. If it's non-linear as said in my book, why does my reasoning which concludes that the differential equation is linear fail? Based on the form of \(r(x)\), we guess a particular solution of the form \(y_p(x)=Ae^{−2x}\). If we consider functions $P$ and $Q$ such that $P=2xf(x)$ and $Q=x^2+f^2(x)$, then we can write the above differential equation as: \begin{align} Solution to first-order non-linear system of ordinary differential equations, Help with linear differential equation problem, Adjoint equation for the second order linear differential equation. The major difference between linear and nonlinear equations is given here for the students to understand it in a more natural way. To learn more, see our tips on writing great answers. But hopefully the intended meaning is clear: functions $P_0, \ldots, P_n,$ and $Q$ are given, and your goal is to find a function $y$ which satisfies $P_0(x) y^{(n)}(x) + \cdots + P_n(x) y(x) = Q(x)$ for all $x$. Q-P~\frac{\mathrm{d}y}{\mathrm{d}x}&=0\\ Complex first-order differential equation. Sharma, defines a linear differential equation as follows: A differential equation is a linear differnetial equation if it is expressible in the form, $$P_0\frac{\mathrm{d}^ny}{\mathrm{d}x^n}+P_1\frac{\mathrm{d}^{n-1}y}{\mathrm{d}x^{n-1}}+P_2\frac{\mathrm{d}^{n-2}y}{\mathrm{d}x^{n-2}}+\dots++P_{n-1}\frac{\mathrm{d}y}{\mathrm{d}x}+P_ny=Q$$. It only takes a minute to sign up. rev 2020.10.7.37749, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, $(x^2+y^2)~\mathrm{d}x-2xy~\mathrm{d}y=0$.