Verify that the function satisfies the differential equation. (A differential equation in $x$ and $y$ is an equation that involves $x, y$ , and derivatives of $y$ .) Function Differential Equation $y = 5 sin (x) + 8 y^{''} + y = 8$ Find $y^{'}$ and $y^{''}$ $y^{n} =$ Substitute $y$ and $y^{''}$ into the differential equation and simplify. $y^{2} + y = (2) + (5 sin (x) + 8) = + 8 = 8$

Question

Verify that the function satisfies the differential equation. (A differential equation in

x

and

y

is an equation that involves

x, y

, and derivatives of

y

.) Function Differential Equation

y = 5 sin (x) + 8 y^{''} + y = 8

Find

y^{'}

and

y^{''}

y^{n} =

Substitute

y

and

y^{''}

into the differential equation and simplify.

y^{2} + y = (2) + (5 sin (x) + 8) = + 8 = 8

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