Closed 7 year ago.
You are watching: What are the arbitrary constants in equation 1?
In general, the number of arbitrary constants of an ordinary differential equation (ODE) is given by the bespeak of the highest possible derivative.
e.g. $$ycolorred"=f(x)$$ has $colorred extone$ constant of integration, $$ycolorred""+y"=f(x)$$ has $colorred exttwo$, $$ycolorred"""+y""=f(x)$$ has $colorred extthree,$ etc..
See more: Bus From Los Angeles To Temecula Ca To Los Angeles Ca And Temecula, Ca
To generalise, intend we"ve an ODE the the form $$a_ny^(colorgreenn)+a_n-1y^^(n-1)+cdots+a_2y""+a_1y"+a_0y=f(x), $$ wherein $a_i$ is a role of $x$.
Then the number of arbitrary constants in the basic solution to this equation is $colorgreenn.$
answer Aug 15 "14 at 18:34
11k1010 gold badges4040 silver- badges6868 bronze title
add a comment |
Not the prize you're spring for? Browse other questions tagged ordinary-differential-equations or asking your own question.
Featured top top Meta
number of arbitrary constant in a Partial differential equation
variety of arbitrary constants in the basic solution of one ODE
Is the true the the variety of arbitrary constants in the solution constantly equal to order that the plain differential equation?
arbitrarily constants in the systems of one ODE
Difference between constants, arbitrarily constants and also variables in differential equation
does the bespeak of a differential equation necessarily equal the variety of arbitrary constants in the general solution?
Differential Equations - Arbitrary and fixed constants
have the right to one prove that there are precisely $n$ arbitrarily constants exist in the solution of a $n$th order differential equation?
number of arbitrary constants in the general solution of a differential equations
hot Network concerns an ext hot inquiries
ridge Exchange Network
site architecture / logo design © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.11.5.40661