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mariask
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so I am trying to solve this equation y'+5.6y=9.5cos(2x)+2.4sin(2x) . I want the c in order to y'(0)=0. I am really lost
There is NO "c" in what you wrote! Do you mean the constant in the solution? It isn't necessarily called "c"!mariask said:so I am trying to solve this equation y'+5.6y=9.5cos(2x)+2.4sin(2x) . I want the c in order to y'(0)=0. I am really lost
An ODE, or ordinary differential equation, is a mathematical equation that describes the relationship between a function and its derivatives. It involves one or more independent variables and the derivatives of the dependent variable with respect to those independent variables.
Solving an ODE means finding a function that satisfies the given differential equation. This involves finding the value of the unknown function at different points in the domain, usually through the use of mathematical techniques and algorithms.
The constant c in an ODE represents the initial condition of the function at a specific point in the domain. In this case, y'(0)=0 means that the derivative of the function at the point 0 is equal to 0. Finding the correct value of c ensures that the solution satisfies this specific initial condition.
There are several methods for solving an ODE, including separation of variables, substitution, and using integrating factors. The method used to find c will depend on the specific form of the ODE and its initial conditions.
Yes, an ODE can have multiple solutions for c. This is because the value of c affects the overall solution of the ODE and can result in different functions that satisfy the given differential equation. It is important to carefully consider the initial conditions and choose the appropriate value of c for the desired solution.