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What are some sample problems in differential equations involving the elimination of the arbitrary constant?
The only way to eliminate the arbitrary constant is if an extra equation is given that gives a value to y at a specific x. Example: Solve the differential equation, dy/dx = 2x + 3, where y = f(x), with condition, f(1) = 3. Separate the variables and integrate: dy = (2x + 3)dx, ∫ dy = ∫ (2x + 3)dx, y + C1 = x2 + 3x + C2. C1 and C2 are arbitrary, so they combine into one constant, C: y = x2 + 3x + C Find C by substituting the values of the given condition into the above equation: 3 = 12 + 3(1) + C = 1 + 3 + C = 4 + C, so C = -1 Our final answer then, with the given condition, is: y = x2 + 3x - 1
What is differential equation in mathematics?
It is an equation containing differentials or derivatives, there are situations when variables increase or decrease at certain rates. A direct relationshin between the variables can be found if the differential equation can be solved. Solving differential equations involves an integration process:first order dy _____ which introduces one constant arbitrary dx And secnd order which introduces two arbitrary constant arbitraries 2 d y ______ 2 d x dx
What is the difference between ordinary constant and an arbitrary constant?
Ordinary constant is a real constant which is same in all time but arbitrary constant is not constant at all time intervals, especially we can see arbitrary constants in integrals.For example the anti derivative of x+C is 1. Here we can replace C with any constant so C is arbitrary constant
How first order derivative zero in differential equations?
Well, 0 is a constant, so the derivative of 0(, or any other constant) is 0. This information is coming from an 11 year old kid.
What are the common characteristic between simultaneous linear equations in 2 unknowns which have no solutions?
The coefficients and constant in one of the equations are a multiple of the corresponding coefficients and constant in the other equation.
