How to verify that each given function is a solution of the differential equation?

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01-09-2022
Mathematics

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How to verify that each given function is a solution of the differential equation?

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KarpaT KarpaT · Answer 1 · 2022-09-06T03:25:12-04:00

Each given function is a solution of the differential equation, when the solution satisfies any equation or inequality by using substitution.

In this question,

A solution to a differential equation is a function y=f(x) that satisfies the differential equation when f and its derivatives are substituted into the equation. Verifying a solution ensures the solution satisfies any equation or inequality by using substitution.

If y = f(x) is a solution to a differential equation, then if we plug 'y' into the equation, we get a true statement. If a true statement is created, meaning that the left-hand side (LHS) of the equation is equal to the right-hand side (RHS) of the equation, then the function is a solution to the differential equation.

Hence we can conclude that each given function is a solution of the differential equation, when the solution satisfies any equation or inequality by using substitution.

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