Explanation Procedure used: Solution to a differential equation: The n th-order ordinary differential equation is one dependent variable by the general form, F ( x , y , y ' , ... , y ( n ) ) = 0 Where F is a real valued function of n + 2 variables: x , y , y ' , ... , y ( n ) . The solution of an n th-order ordinary differential equation is a function ϕ that possesses at least n derivatives and satisfying the differential equation on interval I , (i.e.,) F ( x , ϕ ( x ) , ϕ ' ( x ) , ... , ϕ ( n ) ( x ) ) = 0 for all x in I . Calculation: Consider the given differential equation y ″ = y ′ . The function is a solution to the given differential equation if the function is satisfied by the differential equation. For the function y = a ,where a is a constant The derivative is given as, y ′ = d d x ( a ) y ′ = 0 Again, differentiate the above obtained result, y ″ = d d x ( y ′ ) = d d x ( 0 ) = 0 Compare the obtained values of y ″ and y ′

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Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Differential Equations

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At least one solution of the differential equation y ″ = y ′ by inspection.

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At least one solution of the differential equation y″=y′ by inspection.

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