Verify That Each Function Is a Solution to the Given Differential Equation

In each of the following examples, verify that the given function is a solution of the corresponding differential equation. Solution D.E. y = xn x2d2ydx2-n×xdydx ny=0 -

In each of the following examples, verify that the given function is a solution of the corresponding differential equation. Solution D.E. y = xn x2d2ydx2-n×xdydx ny=0

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$SOLVED:First verify that y(x) satisfies the given differential equation. Then determine a value of the constant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator ( if desired) to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition. y^{\prime}=y 1 ; y(x)=C e^{x}-1, y(0)=5$