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In the following example, verify that the given function is a solution of the corresponding differential equation.
Solution  D.E. 
y = xn  `x^2(d^2y)/dx^2  n xx (xdy)/dx + ny =0` 
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Solution
y = x^{ n}
Differentiating w.r.t. x, we get
`dy/dx = nx^(n1)`
Again, differentiating w.r.t. x, we get
`(d^2y)/dx^2 = n(n1) x^(n2)`
∴ `x^2(d^2y)/dx^2  nxdy/dx +ny`
= n(n1)x^{2}x^{n2}  nx.nx^{n1}+ nx^{n}
= n(n1)x^{n } n^{2 }x^{n} + nx^{n}
=[n(n1)n^{2}+n]x^{n}
= 0
∴ `x^2 (d^2y)/dx^2  nxdy/dx + ny = 0`
∴ Given function is a solution of the given differential equation.
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