Consider the family of functions uc(x,t) of two variables x,t, indexed by the parameter c, uc(x,y)=ln(x+ct)(cos(ct)cos(x)−sen(ct)sin(x)). Determine the value of the parameter c>0 so that the function uc(x,y) is a solution of the wave equation
Consider the family of functions uc(x,t) of two variables x,t, indexed by the parameter c,
uc(x,y)=ln(x+ct)(cos(ct)cos(x)−sen(ct)sin(x)).
Determine the value of the parameter c>0 so that the function uc(x,y) is a solution of the wave equation
The function is a rule that associates or fixes a number to the particular point . If , then the independent variables x, t are called the input of the function, and the dependent variable u is called the output of the function.
An ordinary differential equation is an equation containing independent variables, dependent variables, and differential coefficients of dependent variables with respect to independent variables. If the number of independent variables is more than one, then the differential equation is called a partial differential equation.
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