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It is said that y''=0 gives solution y=c1+c2x.
How?
How?
Y''=0 is a mathematical notation that represents the second derivative of the function y with respect to its independent variable. It indicates that the rate of change of the rate of change of y is equal to zero.
To solve y''=0, you can integrate the equation twice with respect to the independent variable. This will result in a general solution that includes two constants of integration. You can then use initial conditions or boundary conditions to determine the specific values of the constants and obtain a particular solution.
Solving y''=0 can be useful in various fields such as physics, engineering, and economics to model and analyze the behavior of systems that exhibit constant rates of change.
Yes, y''=0 can have multiple solutions depending on the initial conditions or boundary conditions given. These conditions determine the values of the constants of integration and thus, the specific form of the solution.
Yes, there are special methods such as Laplace transforms and power series that can be used to solve y''=0 in certain cases. However, the most common and straightforward method is to integrate the equation twice with respect to the independent variable.