calculus - Difference between constants, arbitrary constants and ...
Apr 23, 2016 · You've got solution of DE. That's function depend of variable. Now exactly you've got family of solutions, because of arbitary constants (if there are initiall conditions, you could find this …
calculus - Arbitrary Constants in Differential Equations - Mathematics ...
Dec 14, 2022 · Question: Trouble understanding which constants are arbitrary and need to be eliminated while forming Differential Equation (DE) from its general solution (In contrast to constants which are …
Arbitrary constants in solutions of differential equations
Sep 10, 2017 · 1 While introducing myself to differential equations, I read that the solution to a differential equation may contain an arbitrary constant without being a general solution. I have been …
Difference between arbitrary constant and free variable
Aug 13, 2023 · Variously calling the placeholder ‘b’ ‘ b ’ a (n arbitrary) constant, a (free) variable, and a parameter —depending on the context, framing and emphasis—is not a contradiction in terms.
Integral: arbitrary constant - Mathematics Stack Exchange
Nov 23, 2015 · The arbitrary constant has to be added whenever you are dealing with indefinite integrals. In other words, if you are told that F F is the antiderivative of a function f f, meaning that
algebra precalculus - Arbitrary constant C, when to resolve it to C ...
Feb 8, 2021 · in the picture on top, we resolve the arbitrary constant from −2C1 2 C 1 to C, by why don't we do so when it is 10 C 10 C (below)? In essence, why isn't y = 10 ex + C y = 10 e x + C correct?
ordinary differential equations - Elimination of Arbitrary Constant ...
Jan 16, 2020 · However, when I try to make an equation to eliminate the arbitrary constants, $\alpha$ and $\beta$, I ended up isolating $\alpha$ and $\beta$ then substitute to the equations above, yet it …
linear algebra - Arbitrary constants - Mathematics Stack Exchange
Sep 11, 2017 · where k k is an arbitrary constant. For what values of k k does the system have a unique solution? I know for this I have to put it in a matrix, but I am having a problem solving the matrix can …
Differential Equation of Elimination of Arbitrary Constant
Sep 17, 2021 · Question: Find the differential Equations having as solution: Eq.1: y=xsin(x+c) Tip: (Elimination of Arbitrary constant) My Answer: First Derivative of Equation 1: By Product Rule dy/dx = …
Why is there a constant of integration? - Mathematics Stack Exchange
Since a a is just some number, F(a) F (a) is also just an arbitrary constant. In that sense, you could see the integration constant as a relic of choosing an arbitrary basis point in your definition of the …