Linear vs nonlinear differential equation - Mathematics Stack …
$\begingroup$ If the ODE has the unknown function and/or its derivative(s) as an argument of a trigonometric, hyperbolic trigonometric, exponential, logarithmic, and/or n-th root function, the ODE is non-linear.
calculus - What is the practical difference between a differential …
See this answer in Quora: What is the difference between derivative and differential?. In simple words, the rate of change of function is called as a derivative and differential is the actual change of function. We can also define a derivative in terms of differentials as the ratio of differentials of function by the differential of a variable.
Is there a reason it is so rare we can solve differential equations?
2020年8月6日 · Compare Differential Equations to Polynomial Equations. Polynomial Equations are, arguably, much, much more simple. The solution space is smaller, and the fundamental operations that build the equations (multiplication, addition and subtraction) are extremely simple and well understood.
reference request - Best Book For Differential Equations?
The differential equations class I took as a youth was disappointing, because it seemed like little more than a bag of tricks that would work for a few equations, leaving the vast majority of interesting problems insoluble. Simmons' book fixed that.
analysis - How to tell if a differential equation is homogeneous, or ...
2015年1月27日 · The simplest test of homogeneity, and definition at the same time, not only for differential equations, is the following: An equation is homogeneous if whenever $\varphi$ is a solution and $\lambda$ scalar, then $\lambda\varphi$ is a solution as well.
partial differential equations - Mathematics Stack Exchange
2020年4月30日 · Why are the Partial Differential Equations so named? i.e, elliptical, hyperbolic, and parabolic. I do know the condition at which a general second order partial differential equation becomes these, but I don't understand why they are so named? Does it have anything to do with the ellipse, hyperbolas and parabolas?
ordinary differential equations - difference between implicit and ...
We aren't always this lucky when we solve differential equations that show up in practice. It often happens that we can only be content with an implicit solution (or a parametric solution, which is a somewhat better state of affairs than having just an implicit solution).
ordinary differential equations - What exactly is steady-state …
We want a theory to study the qualitative properties of solutions of differential equations, without solving the equations explicitly. Moreover, we often want to know whether a certain property of these solutions remains unchanged if the system is subjected to …
Transient terms in the solution of a linear differential equation
2018年2月27日 · ordinary-differential-equations; Share. Cite. Follow edited Feb 27, 2018 at 10:58. MrYouMath. 16k 3 3 gold ...
Differential Equations without Analytical Solutions
The differential equations courses at my university are method based (identify the DE and use the method provided) which is completely fine. However, I'd like to have some examples which look easy (or look similar to ones for which the given methods will work) in order to show students that not all differential equations are so easily solved.