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In each of the Exercises 1 to 10 verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$y=x^{2}+2 x+\mathrm{C}$ $y^{\prime}-2 x-2=0$
Calculus 2 / BC
Chapter 9
Differential Equations
Section 2
Basic Concepts
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University of Nottingham
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The given differential equation is V- -2 X -2 is equal to zero. No we need to check whether the function why is equal to x squared plus two X Plus C. is a solution of this differential equation or not. So let us find the first elevator that is very dash which will be cool too two x plus two and derivative of consent zero. So we get by dash two. B two X plus two. Now let us substitute this and the given differential equation. So let us right by that should be two x plus two minus two X minus two. Opening the brackets, we get two X plus two minus two X minus two. So minus two X cancels it plus two eggs and plus two cancels at minus two. So we get zero there. Will we can see that the given function is a solution of the given differential equation.
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