Determine whether the given function is a solution to the given differential equation.

$y=cosx+x^7,\frac{d^{2}y}{d{x}^2}+y=x^7+42x^5$

The function $y=cosx+x^7$ a solution to the differential equation $\frac{d^{2}y}{d{x}^2}+y=x^7+42x^5,$ because when the second derivative is substituted for $\frac{d^{2}y}{d{x}^2}$ and $cosx+x^7$ is substituted for $y,$ both sides of the differential equation $$ equivalent