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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
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How do you solve equations involving fractional coefficients?
multiply the whole equation by the number in the denominator
Can computer solve exponential function?
Do you mean "equations involving exponential functions"? Yes,
Steady state in partial differential equations?
In the context of partial differential equations (PDEs), a steady state refers to a condition where the system's variables do not change over time, meaning that the time derivative is zero. This implies that the solution to the PDE is time-independent, and any spatial variations in the solution remain constant. Steady state solutions are often sought in problems involving heat diffusion, fluid flow, and other dynamic processes to simplify analysis and understand long-term behavior. In mathematical terms, steady state can be represented by setting the time-dependent term in the governing equation to zero.
Literal equations involving letters?
1/x=c+1/b, solve for x x=c+b/1
What has the author Sudakhar G Pandit written?
Sudakhar G. Pandit has written: 'Differential systems involving impulses' -- subject(s): Differential equations, Perturbation (Mathematics)
What is the difference between a homogeneous and a non-homogeneous differential equation?
a linear first-order differential equation is homogenous if its right hand side is zero & A linear first-order differential equation is non-homogenous if its right hand side is non-zero.
Give some examples where Quadratic equations is used in daily life?
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What is the different rules involving equations?
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What are the Uses of Cauchy Euler equation?
One thing about math is that sometimes the challenge of solving a difficult problem is more rewarding than even it's application to the "real" world. And the applications lead to other applications and new problems come up with other interesting solutions and on and on... But... The Cauchy-Euler equation comes up a lot when you try to solve differential equations (the Cauchy-Euler equation is an ordinary differential equation, but more complex partial differential equations can be decomposed to ordinary differential equations); differential equations are used extensively by engineers and scientists to describe, predict, and manipulate real-world scenarios and problems. Specifically, the Cauchy-Euler equation comes up when the solution to the problem is of the form of a power - that is the variable raised to a real power. Specific cases involving equilibrium phenomena - like heat energy through a bar or electromagnetics often rely on partial differential equations (Laplace's Equation, or the Helmholtz equation, for example), and there are cases of these which can be separated into the Cauchy-Euler equation.
What is a linear system and how does it relate to mathematical equations?
A linear system is a set of equations involving multiple variables that can be solved simultaneously. These equations are linear, meaning they involve only variables raised to the first power and do not have any exponents or other non-linear terms. Solving a linear system involves finding values for the variables that satisfy all of the equations in the system at the same time. This process is often done using methods such as substitution, elimination, or matrix operations.
What is the definition of Simultaneous Linear Equations?
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
How do you solve two-step equations with fractions?
Equations can be tricky, and solving two step equations is an important step beyond solving equations in one step. Solving two-step equations will help introduce students to solving equations in multiple steps, a skill necessary in Algebra I and II. To solve these types of equations, we use additive and multiplicative inverses to isolate and solve for the variable. Solving Two Step Equations Involving Fractions This video explains how to solve two step equations involving fractions.
How can you solve problems involving equivalent expressions?
In the same way that you would solve equations because equivalent expressions are in effect equations
What are the geometric problems involving linear equation?
i want an example of geometric linear equations
How do you solve equations involving fractional coefficients?
multiply the whole equation by the number in the denominator
Can computer solve exponential function?
Do you mean "equations involving exponential functions"? Yes,
